Imitative research and development in the neo-Schumpeterian theory of growth


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Imitative research and development in the neo-Schumpeterian theory of growth
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Houser, Cindy, 1960-
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Thesis (Ph. D.)--University of Florida, 1995.
Includes bibliographical references (leaves 128-134).
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by Cindy Houser.
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This dissertation would not be possible without the experience, enthusiasm and

generosity of many. Elias Dinopoulos provided valuable guidance and made many

course corrections along the way. Richard Romano and Doug Waldo contributed

essential perspective on style, presentation, and logical consistency. Each, by example

and advice, also introduced me to the art of teaching. Peter Thompson often played the

devil's advocate, forcing me to rethink and refine my arguments. I thank these people

for their assistance and many others who helped in my studies.



ACKNOWLEDGMENTS ....................................ii

ABSTRACT ......................................... .vii



1.1 Introduction ...................... ..... ...... 1
1.2 A Stability Consideration .... .. ................6
1.3 Imitation and Trade Among Advanced Countries .......... 8
1.4 Imitation and International R&D Knowledge Spillovers ...... 10


2.1 Introduction ..............
2.2 Introducing Specific Factors .
2.2.1 The Model ............. Consumer behavior .... Asset market ........ Production and entry . Research and development Innovation .......... Imitation ...........
2.2.2 Market Equilibrium ....... Product market ....... Labor market......... Specific factors .......
2.2.3 Steady-State ........... Characteristics ....... Industrial targeting ... Zero-profit conditions . Steady-state equilibrium .

. . . 13
. . . 15
. . . .15
. . . .17
. . . .18
. . . 18
. . . .20
. . . 2 1
. . . 2 1
. . . .22
. . . .22
. . . .23
. . . 23
. . . .24
. . . .24
. . . 24
. . . 25
. . 26
. . . .27

2.3 Stability and Comparative Statics ................... .28
2.3.1 Stability ................ ................. 29
2.3.2 Comparative Statics ................... 34
2.4 Restrictions and an Example . . ... 35
2.4.1 Restrictions .............................. 35
2.4.2 Example ............... ...............37
2.5 Conclusion ................................37


3.1 Introduction .......................... .......39
3.2 World Economy ................ .......... .42
3.2.1 Overview ............................. 42
3.2.2 Consumer Behavior ................... ... ..43
3.2.3 Product Markets ......................... 43
3.2.4 Innovative R&D ......................... .44
3.2.5 Imitative R&D ........ .................. .45
3.2.6 Labor Market ........................... 46
3.2.7 Industrial Targeting ......................... 47
3.2.8 Steady-State Equilibrium ................. .47
3.3 Welfare and Comparative Statics ................... .. 53
3.4 Trade and Technology Transfer .................... .55
3.4.1 Assumptions/Trading Framework ............... 55
3.4.2 Factor Price Equalization Set ................... .59
3.4.3 Trade Patterns ................... ......... 62
3.5 Conclusion .................................67


4.1 Introduction ... .................. ............69
4.2 W hat Are Spillovers? ...........................72
4.3 Acquired Knowledge Or Spillovers? ................. 76
4.4 Measuring Spillovers .......................... 85
4.5 Conclusion ............................... 89

5. WHAT'S NEXT ? .................... .... ........ 91


A. CONSUMER PROBLEM ........................... 96
A.1 Derivation of Equation 2.3 ..... ............ 96
A.2 Derivation of Equation 2.4 .................... 98


C.1 Chapter2 ................................ 102
C. 1.1 Proof that Quality Leaders in a Industries Won't
Engage in Innovative R&D ...................... 102
C.1.2 Proof that a Quality Leader in a 0 Industry Will Not
Innovate ................................... 104
C. 1.3 Proof that a Previous State-of-the-Art Quality Producer
Does Not Have an Incentive to Engage in Innovative R&D in
an a Industry ...................... ......... 105
C. 1.4 Proof that a Previous State-of-the-Art Quality Leader
Will Have No Incentive to Innovate in a 0 Industry. ........ 105
C. 1.5 Proof that a Competitive Fringe Firm Will Not Engage
in Innovative Activity in an a Industry .............. .105
C.2 Chapter 3 .................................... 106
C.2.1 Proof that Quality Leaders in a Industries Won't
Engage in Innovative R&D ......................107
C.2.2 Proof that a Competitive Fringe Firm Will Not Engage
in Innovative Activity in an a Industry ... ........ 108
C.2.3 Proof that Quality Leaders Will Not Innovate in a 0
Industry ......................................... 109
C.2.4 Proof that Previous Quality Leaders Will Have No
Extra Incentive to Innovate ................. .. 109

D. PROPERTIES OF REDUCED FORMS ................. 111
D.1 Chapter2 .... ..... ............. ........... 111
D.1.1 Properties of C (I) ..................... .... 112
D.1.2 Properties of C (I) ..........................112
D.1.3 Intercept Terms for Figures 2.2 and 2.3 .......... .113
D.2 Chapter3 .............. ................... 114
D.2.1 Characteristics of I = 0 ................... .114
D.2.2 Characteristics of C = 0 ..................... .115
D.2.3 Comparison of Co and C, .................... 115
D.2.4 Characteristics of Czc(I) ................... 116

E. DERIVATION OF PHASE DIAGRAMS ................ 117

F. COMPARATIVE STATICS ..........................119
F.1 Subsidy to Innovation ................. .........119
F.2 Subsidy to Imitation .............. ....... ......... 120

G. WELFARE ANALYSIS .................. ........121
G.1 Derivation of the Growth Rate of Instantaneous Utility ..... 121

G.2 Derivation of Welfare ......................... 122
G.3 Welfare Properties of the World Economy ............. .122

H. ENDOWMENT REGIONS ................. ........ 126

REFERENCES ..........................................128

BIOGRAPHICAL SKETCH ........................... ........ 135

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Cindy Houser

August 1995

Chair: Elias Dinopoulos
Major Department: Economics

This dissertation explores endogenous technology transfer through imitation. The

context is a dynamic general equilibrium model of growth generated by innovation.

Segerstrom extends the one-factor quality ladders model of Grossman and Helpman by

incorporating endogenous imitation. Comparative static experiments produce perverse

results. An increase in a subsidy to innovative (or imitative) activity reduces the level

of innovative (or imitative) activity. In Chapter 2. I show that Segerstrom's model is

unstable because of linear research and development (R&D) unit costs. This instability

causes the perverse results.

By introducing specific factors to innovation and imitation. I obtain instantaneous

diminishing returns to R&D technology at the aggregate level, while still allowing for

constant returns to scale at the firm level. I then derive sufficient conditions for stability

requiring a certain level of instantaneous diminishing returns to R&D activity. The

satisfaction of these conditions assures the 'usual' comparative static results of subsidies

to either type of R&D: an increase in a subsidy to innovative (or imitative) activity

increases innovative (or imitative) R&D activity.

In Chapter 3, I develop a one-factor general equilibrium model of global growth.

I analyze trade among advanced countries in a two-country, integrated equilibrium, world

economy. Risky and costly imitation is the only channel of technology transfer across

countries. The patterns of trade and technology transfer fluctuate stochastically in each

industry and exhibit product cycles and endogenous two-way international technology

transfer. These trade and transfer patterns depend on relative national labor endowments.

I investigate the relevance of knowledge spillovers for theory and policy in

Chapter 4. and examine the struggle of recent empirical efforts to measure the magnitude

and extent of spillovers. These studies do not distinguish between research efforts aimed

primarily at incremental improvements (or imitation) and R&D directed at being first to

bring out the next major product line (or innovation). As a result, they may produce

biased estimates of spillovers from foreign R&D. I argue that intraindustry technology

(or ,.nowl Icdee) transfers are aLgre.sit el acquired rather than passively 'spilled.'


1.1 Introduction

[Ijf we can learn about government policy options that have
even small effects on the long-term growth rate, then we
can contribute much more to improvements in standards of
living than has been provided by the entire history of
macroeconomic analysis of countercyclical policy andfine-
runiing. Economic growth ... is the part of macroeconomics
that really matters.
Barro and Sala-i-Martin (1995, p.5)

Nature moves inexorably forward, renewing, refining, replacing--so does

humanity. From the first rudimentary scraping knifes and the taming of fire to the

Hubble telescope and the splitting of the atom, we never cease our search for a better

way to get what we want, or more of it. We have more and better things every year.

In the language of economics, this is growth. It has been a staple of economic study

since the days of Adam Smith. This field, dominated by Neoclassical growth theory for

years. is enjoying a current renaissance, the focus shifting from analyzing capital

accumulation to understanding technological change.

The Neoclassical theory of growth is based on the Solow (1956) Swan (1956)

neoclassical production function model, as integrated with Ramsey's (1928) treatment of


household optimization by Cass (1965) Koopmans (1965).' It predicts a per-capita

growth rate that converges, in the long run. to an exogenous rate of technical change.

Neoclassical growth theory provides the comforting assertion (to the Neoclassical

economists) that the competitive outcome is Pareto optimal. In fact. there is no

government policy tool that would increase the long-run growth rate in the Neoclassical

model. The Neoclassical theory also explains several empirical stylized facts, including

per-capita output growing over time. physical capital per worker growing over time, and

conditional convergence in growth rates of output (conditional on such factors as initial

human capital levels, government policy, and trade policy).-

The Neoclassical growth theory has some key weaknesses, however. The long-

run growth rate of per-capita income is explained solely by exogenous technical change--

that mysterious little black box. Also, Neoclassical growth theory does not satisfactorily

explain large differences in living standards, development experiences, and growth rates

across countries. Comparison of the East Asian Tigers to the countries of Sub-Saharan

Africa leaves the strong impression that, contrary to the dictates of Neoclassical theory.

government economic policy and trade regime do matter. These weaknesses, combined

with technical advances in mathematical modelling (e.g., imperfect competition).

encouraged the assault on neoclassical growth theory by endogenous growth theory.

'For full treatments of the Neoclassical theory of growth, see the relevant chapters
in Barro and Sala-i-martin (1995), Blanchard and Fischer (1992), or Grossman and
Helpman (1992).

"See Barro and Sala-i-Martin (1995. Ch 1.2)


The objective of the new growth theory is not to describe the mechanics of growth

but to explain its causes. Thompson provides these criteria for endogenous growth


C.1. Endogenous growth models must permit a non-
zero long-run rate of per-capita welfare growth.
C.2 The long-run rate of growth must be a function of
choice variables in the model. (1994, p.l)

There are three main knowledge-based engines of the new growth theory: The

human capital accumulation model (as most recently popularized by Lucas [1988]) bases

growth on the individual decisions of agents investing in education. Learning-by-doing

models (Romer [1986], Lucas [1988], [1993]) envision improvements in technique as a

result of accumulated production experience. Finally, there are models that explain

growth as an outcome of investments by firms in research and development (R&D).

It is a subclass of the latter type of endogenous growth model--Neo-

Schumpeterian--which is the focus of this dissertation. Solow suggests that

the real value of endogenous growth theory will emerge
from its attempt to model the endogenous component of
technological progress as an integral part of the theory of
economic growth. (1994, p.51)

The Neo-Schumpeterian theory of growth aspires to exactly this. Its name arises because

it formalizes Schumpeter's (1942) view of creative destruction as the engine of growth.

Creative destruction is the process by which new goods are brought to the market.

eroding the profits of producers of older goods.

Schumpeter's ideas have been studied at the microeconomic level for some time.

The most useful models for adaption to general equilibrium models of growth are the


stochastic R&D race models of Loury (1979), Dasgupta and Stiglitz (1980a,b), Lee and

Wilde (1980), and Reinganum (1985). These models capture the formal investment

activities in research and development by firms attempting to maximize profits, the

uncertain nature of such investments, and the prospect of winners and losers in

contestable markets. General equilibrium models of monopolistic competition, such as

that of Dixit and Stiglitz (1977). provide a vehicle for integrating these models into

growth theory. An early endogenous growth model along this line is that of Grossman

and Helpman (1989): successful innovators discover new varieties of goods, increasing

consumer utility over time. Since goods are imperfectly substitutable, however, no good

is ever replaced.

The first dynamic general equilibrium models to capture the process of creative

destruction are those of Segerstrom. Anant, and Dinopoulos (1990) and Aghion and

Howitt (1992). Elements of these two models are incorporated into a quality ladders

model by Grossman and Helpman (1991b). Innovations are modeled as Poisson

processes. There is free entry into stochastic R&D races in each industry. One winner

discovers how to produce a product of superior quality. Concurrent races across a

continuum of industries result in a certain and continuous growth rate of aggregate

consumer utility. As Thompson (1994) points out. market externalities in these models

move the competitive equilibrium away from the socially optimal outcome. An

appropriability effect occurs, whereby the innovator cannot capture all social benefits:

an intertemporal spillover effect exists because the benefits of an innovation last forever.


but the firm doesn't. An R&D subsidy or tax can achieve the socially optimal outcome.

but there is no consensus on which is needed.

A second prominent feature of technical change to consider is technological

diffusion--particularly imitation. Baldwin and Scott distinguish between imitation and

dissemination--voluntary technology transfer by the innovator (say through licensing):

Unauthorized imitation is a major diffusion mechanism
when patents are easily circumvented, when high litigation
costs and uncertainties make patents little more than a
"license to sue," and when "reverse engineering," or the
analysis of how a competitor's product was made, is
routinely pursued. Imitation may in some circumstances
augment the net social benefits from innovation by
speeding diffusion and expanding an innovation's ultimate
spread toward the output level where the marginal social
cost of adoption equals the marginal social benefit. But,
alternatively, by reducing anticipated earnings, imitation
may retard the incentive to innovate. (1987. p. 120)

This concept has also been studied in depth at the microeconomic level. Some of the

important theoretical works which sought to understand the relationship between market

structure, innovation, and imitation were Scherer (1967). Kamien and Schwartz (1978)

and Nelson and Winter (1982). These efforts have uncovered a variety of possible

strategic situations: market power may encourage or inhibit imitation and imitation may

foster or discourage market concentration.

Several key empirical case studies by Mansfield et al. (1981), Mansfield et al.

(1982), and Mansfield (1985) conclude that imitators typically take 70 percent of the time

and spend 65 percent as much on R&D as the innovator; imitation lags are between one

and two years; patents raise the costs of imitation but don't reduce its occurrence: the


expectation of rapid imitation does not discourage innovative activity: and cross-country

imitation lags may be declining due to improvements in communication, transportation.

and the increased relative importance of more easily imitated products such as software.

Imitation is an important phenomenon.

Several Neo-Schumpeterian models of growth encompass the possibility of

imitation. These are, almost exclusively, two-country models that examine various issues

of North-South trade. The primary model is Grossman and Helpman (1991b). In their

model, only the North innovates: the South gains market share by imitating and captures

the market because of lower wages. This model was generalized and used to examine

such issues as property rights protection (Helpman [1993]. Taylor [1993a,b], [1994])

and. partial market penetration (Glass [1992]). Far less work examines imitation and

trade between advanced countries. One exception, incorporating exogenous imitation into

a Heckscher-Ohlin model with endogenous innovation, is Dinopoulos et al. (1993). One

of the goals of this dissertation is to endogenize imitation in a model of trade between

advanced countries. I regard this as an essential step in understanding the role of

technology transfer at all stages of world development.

1.2 A Stability Consideration

Segerstrom (1991) develops a closed economy Neo-Schumpeterian model of

endogenous innovation and endogenous imitation. The difficulty in endogenizing

imitation is the necessity of positive expected economic profits in final goods production


to provide motivation for the potential imitator to enter into costly and risky imitative

activity. In the North-South model, this is simply a matter of postulating differences in

production capabilities across countries. It is a little more difficult in a closed-economy

model. Segerstrom proves the existence of a steady-state Nash equilibrium in which

imitators can expect to collude with the market leader and earn positive profits. I extend

this model to a two-country version in which technology transfer occurs through

endogenous imitation. First, however, a stability analysis proves necessary.

In Segerstrom's model, innovation and imitation are modelled as Poisson

processes: there is free entry into both innovative and imitative R&D races, there is one

factor of production, and unit labor requirements in each activity are constant. This

model, however, has unusual comparative static results: a subsidy to innovation lowers

the per industry level of innovative activity. Concurrently, a subsidy to imitation lowers

imitative activity. In Chapter 2, I show that this arises from the assumption of constant

unit labor requirements. By introducing specific factors to each activity, I allow for

instantaneous diminishing returns to R&D and show that. when there are sufficient

diminishing returns, the comparative static results are reversed: a subsidy to innovation

increases the level of industry innovative activity. Similarly, a subsidy to imitation

increases the level of imitative activity.

In the spirit of Samuelson's Correspondence Principle. I relate the above result

to a stability analysis. I introduce ad-hoc adjustment mechanisms. These require entry

into or exit from R&D races when expected discounted profits are not equal to expected

discounted costs, as required for equilibrium. I find that, when instantaneous diminishing


returns to R&D are not sufficient, the model's only interior solution is locally unstable.

This necessity of diminishing returns accords with several empirical studies. See

Thompson (1995b) for an empirical study of. among other things, instantaneous returns

to R&D in a Neo-Schumpeterian model. He finds strong evidence for diminishing

returns. As it turns out, introducing diminishing returns to R&D imposes no great

limitation on the usefulness of the models involved. I incorporate instantaneous

diminishing returns into the two-country model of Chapter 3 of this dissertation, and

study the implications of endogenous imitation for trade patterns.

1.3 Imitation and Trade Among Advanced Countries

Trade economists have long preached the virtue of free trade, but empirical

studies have usually reported only minor static welfare losses resulting from trade

restrictions.3 The new growth theory may validate the trade theorists' policy

recommendations, however, with the possibility of large dynamic effects of trade policy.

Romer (1993b) shows that, in a country where lifting trade restrictions can introduce

new goods into the economy, the potential welfare benefits are an order of magnitude

larger than traditional welfare loss measurements. Trade restrictions can also reduce the

size of potential profits to innovation, lowering the rate of innovation and growth.

3See Feenstra (1992) for a discussion of the empirical measurement of welfare


Another benefit of the new growth models is the ability to explain changing trade

patterns over time. The North-South trade models formalize Vernon's (1966) description

of the product cycle. Production of new goods, introduced in the North, is eventually

transferred to the South to take advantage of lower production costs. Dinopoulos et al.

(1993) develop a dynamic version of the two-country Heckscher-Ohlin model. Growth

is driven by endogenous innovation, and trade patterns are influenced by innovation and

exogenous imitation. Interindustry and intraindustry trade, product cycles and

multinationals are possible, but technology transfer is exogenous, costless, and can only

occur in one direction, contrary to the evidence.4

Chapter 3 extends the model of Chapter 2 to a two-country integrated equilibrium

world economy in which factor price equalization occurs. The model is simplified by

assuming that there is now only one factor of production. Each R&D activity has a

specific functional form exhibiting instantaneous diminishing returns to R&D. There is

also an exogenous diffusion effect, introducing the possibility that imitative R&D activity

has a positive welfare effect aside from any competitive or variety effects in the final

goods market. Technology transfer can only occur through costly imitation. Two-way

technology transfer and trade patterns depend on relative national labor endowments.

4See the various studies by Mansfield cited above and the survey of Nadiri (1993),
which enumerate the expenses incurred in efforts to transfer technology from one country
to another, both cooperative and noncooperative.

1.4 Imitation and International R&D Knowledge Spillovers

With the advent of endogenous growth literature, R&D knowledge spillovers have

come to play an important role in growth theory. Long-run growth in utility.

productivity or per-capita income is still driven by technological Jhange. but

technological change is endogenized in the Neo-Schumpeterian literature. It arises from

investment in R&D. But, are there long-run diminishing returns to R&D, as there are

to additions to the capital stock?5 Formal Neo-Schumpeterian modelling generally side-

steps this question by assuming that, in the steady-state, the expected costs of discovering

each new higher quality product are no larger than the expected costs of discovering the

last. Each new increment in knowledge is achieved at constant cost. This assumption

of constant returns to scale (CRS) in R&D is justified by the notion that there are

spillovers of knowledge from current innovations that aid in subsequent innovations and

exactly offset any long-run diminishing returns. There is no attempt to identify the

mechanisms by which these spillovers are accomplished.

In addition to the importance of spillovers in long-run growth. Neo-Schumpeterian

literature also assigns importance to them in interactions among countries. Generally,

anything which increases the profitability of national R&D increases growth. Thus, the

5These long-run diminishing returns to R&D should be distinguished from the
instantaneous diminishing returns to R&D discussed above. The former occurs, for
example, if a given stock of basic knowledge offers a fixed amount of exploitable ideas.
Although basic research is often considered to have nondecreasing long-run returns ( See
Romer [1993b]), it may or may not accumulate fast enough to counteract diminishing
returns to the current stock. Instantaneous diminishing returns can occur at the industry
level if there are fixed factors, such as skilled labor, in R&D activity.


importance of free trade comes to the forefront of policy discussions because of the large

potential growth effects of increases in market size. It is also true that policies which

increase the effectiveness of accessing foreign knowledge, thus increasing the

productivity of home R&D efforts, will accelerate growth." These may or may not be

free trade policies. Whatever the case, it seems advisable to delve deeper into the

nature of international R&D knowledge spillovers.

Recent empirical literature tries to quantify the magnitude and extent of

international R&D spillovers. Two key related questions are at the center of attention:

Is there a significant geographic dimension which may imply advantage to the country

of origin for any given innovation? What is the relative contribution to. say, productivity

growth of domestic and foreign R&D efforts? Griliches (1992) surveys the literature and

concludes that R&D spillovers are both prevalent and important. Nadiri (1993), in an

extensive survey, concurs, citing evidence that finns must incur R&D expenses to realize

the benefits of knowledge spillovers, and presenting findings that spillovers may be

stronger within than among countries. Irwin and Klenow (1994). however. present

evidence that spillovers flow freely across borders. Coe and Helpman (1993) conclude

that spillovers to trading partners amount to 25 percent of the world return to R&D

conducted by the seven largest OECD economies. A ubiquitous finding of this type of

"See Dinopoulos and Kreinin (1994), Ruffin (1994) and Brecher. Choudri and
Schembri (1994) for examples of models that exhibit this effect.

7Irwin and Klenow's study looks at the semiconductor industry because it is
considered a strategic industry. The study uses data on average industry selling price and
firm shipments. The findings on spillovers lead the authors to conclude that there is no
justification for a national R&D subsidy to that industry.


study is that foreign R&D has a stronger total effect on factory productivity than

domestic R&D.

The theoretical implications of the model developed in Chapter 3 suggest a more

complex relationship between trade and international R&D knowledge spillovers than

implied by most existing studies. In particular, the model implies that some R&D

expenditures are innovative and some imitative. I argue in Chapter 4 that ignoring this

difference introduces bias into estimates of the magnitude of spillovers, and leads to

misinterpretation of the relative contributions of foreign and domestic R&D. I first

discuss the concept of spillovers in depth, stressing the need for engaging in R&D

activity in order to capture true spillovers of knowledge from the R&D activities of

others. I next develop an equation of knowledge accumulation and technology transfer

consistent with the model of Chapter 3 and compare it to some existing literature. The

chapter concludes with some thoughts on the measurement of spillovers.


2.1 Introduction

The new growth literature is experiencing a few growing pains. Economists' use

of new mathematical tools opens up new modeling possibilities unparalleled in traditional

Solovian growth models, yet the simplifying assumptions which make these models

workable sometimes lead to trouble. Devereux and Lapham (1994), for example, discuss

a stability problem in the knowledge-driven model of new product innovation of Rivera-

Batiz and Romer (1991). A branch of Neo-Schumpeterian growth theory, beginning with

the work of Grossman and Helpman (1991b), has a similar stability problem. This

chapter shows that introducing instantaneous diminishing returns to R&D activity resolves

the stability problem.

Recall from Chapter 1 that Segerstrom (1991) extends Grossman and Helpman's

(1991b) model of quality growth. He incorporates endogenous innovative and imitative

R&D activities into a closed-economy one-factor model of growth. It is one of two Neo-

Schumpeterian models of growth incorporating endogenous imitation.' The model

generates counter-intuitive comparative static results: when a subsidy to innovative R&D

SThe alternative is the product cycle model of Grossman and Helpman (1991a).



is introduced, the intensity of innovative activity falls. The same is true of a subsidy to


This chapter shows that these perverse comparative-static results arise because

the model is unstable. The problem is the use of linear R&D unit costs. By introducing

a more general cost function. I show that the instability can be eliminated and the unusual

comparative static results reversed. This occurs when there are sufficient instantaneous

diminishing returns to R&D. Segerstrom (1994) and Cheng and Tao (1993) address

similar issues. Segerstrom shows that the quality ladders model of Grossman and

Helpman (1991b) is not stable when all industries are not subsidized and uncertainty

about which industries will be subsidized exists. Cheng and Tao replace the linear costs

of Segerstrom (1991) with quadratic costs and show that this reverses the comparative

static results. They do not conduct a stability analysis or derive stability conditions.

This chapter looks explicitly at the relationship between the stability analysis and the

comparative static results.

Section 2.2 sets out the model and establishes the existence of equilibrium

(Proposition 1). Section 2.3 examines the stability of the model and develops the

connection with the comparative static results of subsidies to innovation and imitation

(Proposition 2). Section 2.4 provides a numerical example. A final section offers

concluding remarks.

2.2 Introducing Specific Factors

2.2.1 The Model

This is a dynamic general equilibrium model with a final goods sector and an

R&D sector. Quality-improving innovations occur stochastically over time in a

continuum of industries producing final goods. These, in turn, augment utility because

firms cannot appropriate all of the returns to innovation. A representative agent has a

Cobb-Douglas instantaneous utility function with perfect substitutes (CDP). The agent

maximizes utility over time and over the continuum of final goods. Profit-maximizing

firms use consumer savings to hire labor and undertake R&D.

There are two types of R&D, both of which are modeled as Poisson processes.

Costly and risky innovative R&D is undertaken in each industry, under conditions of free

entry, by firms hoping to be the first to discover the next highest-quality product and

enjoy temporary monopoly profits. Following this innovation, costly and risky R&D is

undertaken in each industry to copy the latest state-of-the-art product. The firm learning

how to duplicate the product first is able to share collusive profits with the leader in the

industry. Growth in consumer utility is endogenously generated by firms choosing R&D

expenditures optimally.

There are three factors of production. Production of final goods exhibits CRS

in labor. Entry into final goods production, however, requires the successful acquisition

of knowledge (innovation or imitation). In addition to labor, the production of innovative

activity requires a fixed specific factor, capital, as does the production of imitative


activity.2 Both factor markets are competitive, and CRS prevails in both R&D activities.

In the presence of fixed factors, however, both innovation and imitation will exhibit

aggregate industry instantaneous diminishing returns to R&D.

In the steady state, consumer expenditures, the interest rate, and the percentage

of industries with one quality leader are constant. The intensities of innovative and

imitative activity are also constant. Innovation and imitation are exponentially distributed

events. The pace of these events is governed by the constant intensity of R&D efforts.

In the steady-state equilibrium, the market structure of each industry alternates between

a monopoly targeted for an imitation race and a duopoly threatened by an innovation

race. Although the current quality leaders) capture the entire market in each industry.

producers of previous state-of-the-art goods force limit pricing on the monopolist and/or

collusive duopoly.

There are R&D knowledge spillovers from innovation to imitation because the

unit costs of imitation are always lower in the steady state than the unit costs of

innovation. There are also exogenous R&D spillovers from one product cycle to the next

because the expected costs of successively larger innovations stay constant. These

spillovers will be discussed, in depth, in Chapter 4. In the next several pages, the

model is briefly developed.

'That innovation and imitation activity may have specific capital in the short run has
support in the literature. It is often different types of firms that innovate and imitate.
See Baldwin and Scott (1987). See also Jovanovic and MacDonald (1994) who argue
that innovation and imitation are substitutes in that firms may compete for market share
by either method. Consumer behavior

A continuum of final goods industries is indexed by w E [0,1]. Each industry

has an countably infinite number of potential qualities, j =0.1 ..., increasing in j. Only

a subset of these qualities has been, as yet, discovered at time t. A representative

infinite-lived consumer maximizes lifetime utility, given by

U fe '"z(t)dt (2.1)

with subjective discount rate p and instantaneous utility

z(t) JI.n Iy XJd(w) dw (2.2)

in which d,,(w) is the quantity consumed at time t. in industry o, of quality j. The

measure of quality improvement of the j* quality over the j-l" quality is X, which is

greater than one by assumption. Let h,(w) represent the state-of-the-art quality at time

t in industry w. Then, it increases utility relative to the lowest quality available by Ah

Because of the stochastic nature of innovation, ht(w) will vary across industries.

As indicated in the next subsection, the current quality leaders) can always

capture the market by charging a limit price determined by its degree of quality

advantage because, given equal quality-adjusted prices, the consumer is assumed to

choose the highest quality available. The instantaneous demand function maximizes

instantaneous utility for given instantaneous expenditures. E(t):

E(t) if
E(t if j h,(o)
d,.(m) Pi,(W) (2.3)
0 else


The price, at time t. of the j' quality in industry w, p,,(w). is taken as given by the

consumer. The time path of expenditure that maximizes lifetime utility is

Aggregate expenditure is determined in the steady state by the value of assets, and r(t)

is the instantaneous interest rate. Equations 2.3 and 2.4 are derived in Appendix A. Asset market

In the asset market, savings are supplied to firms to finance R&D expenditures.

In a typical R&D race, each firm issues a stream of Arrow-Debreu securities for the

duration of the race. The proceeds are just enough to cover the firm's R&D

expenditures. Each security pays out the expected discounted profits of the successful

firm, contingent on the firm winning the R&D race at the instant the security is issued,

and zero otherwise. Since there is a continuum of industries, the industry-specific

uncertainty involved with R&D can be eliminated by the consumer who invests in

diversified mutual fund portfolios. In the steady-state equilibrium, the instantaneous

interest rate equals the riskless rate.' Production and entry

As the name implies, a property of the CDP utility is that. at equal quality-

adjusted prices ( pi,()/ 1 pi,())/l' ), consumers are indifferent to the various

available qualities within an industry. Assume that indifferent consumers will always

choose the higher quality. Take labor as the num6raire so that w = wage = 1. Since

'See Dinopoulos (1994) for a detailed explanation of the asset market in these types of


previous quality producers are willing to supply at marginal cost (p= 1), current leaders

can only markup the price by as much as the consumer values the current quality over

the previous quality. A price higher than X is never optimal since the within-industry

price elasticity of demand is infinite, meaning the consumer would switch entirely to the

lower quality. So, p = X in each industry at all times in the steady state. Appendix C

shows that, in this model, an industry leader never leads by more than one step up the

quality ladder because leaders never innovate. This is not as unreasonable a

characteristic, empirically, as it sounds because, as discussed below, this is a model of

major innovations.

Final goods production is such that one unit of output is produced by one unit of

labor for all products and qualities. To produce the final good, however, firms must

learn how to do so by investing in R&D and winning innovative R&D races. The first

firm to innovate in industry a becomes the sole producer in that industry. This industry

is then targeted for an imitative R&D race. The winner will learn how to copy the

production method of the latest quality product and collude with the current leader.4 The

next round of innovative R&D races will result in discovery of the next quality level, a

new industry leader and so on.

'Segerstrom(1991) proves that a Nash equilibrium steady state exists in which imitators
collude with quality leaders in the production of final goods and so can expect to make
positive profits. The latter is required for costly imitative R&D activity to exist. This
specification of imitation is made for simplicity. An alternative specification in which
imitation is in the form of horizontal differentiation is taken up in Dinopoulos (1992). Research and development

By engaging in i (or c) units of innovative (or imitative) activity each moment.

a firm 'buys' the probability idt (or cdt) of successfully carrying out the next innovation

(or imitation) in the industry in the interval dt. I (or C) is the total level of innovative

(or imitative) activity in each industry targeted for innovation (or imitation) at each

moment.5 Idt is the constant probability that. if the innovation does not occur by time

t. it will by time t + dt. The time duration of each R&D race is exponentially

distributed in the steady state: the hazard rate is the intensity of R&D activity (I or C).

Innovation and imitation races in each industry are subject to free entry, which will occur

until expected discounted profits are driven to zero.

The specific factors in R&D are not specific to an industry but to a particular

activity--innovation or imitation. This implies aggregate diminishing returns to each

activity. Since there is a continuum of industries. no one industry (or firm) is large

enough to affect the returns to the specific factors. All industries are identical, however.

so a representative industry can be thought of for which the specific factor is fixed in the

steady state. This is because the fixed endowment of each specific factor is employed

equally among the fraction of industries .targeted for innovation or imitation. In the

steady state this fraction is constant. Firms are atomistic in each industry at this stage

and can hire labor and capital freely. The number of firms cni aged in R&D is

indetenninant. but not the number of producers.

'To avoid cumbersome notation, and because I and C are constant in the steady state.
I and C are not explicitly shown to be functions of time. Innovation

Labor employed in innovative activity in each industry is L, K, is capital

employed, and I is the intensity of innovative activity for the representative industry

targeted for innovation. Production can be described by the unit cost function. Let w,

be the return to capital, aL the unit labor requirement. and aKI the unit capital

requirement (w,, aU, and aK, are shown, in Appendix B. to be functions of I). Firms are

assumed to be atomistic. capital is fixed, and a Cobb-Douglas production function is

adopted for convenience. Appendix B derives the following expression for unit costs:

lI 1 LI w adKI l," (2.5)

In equation 2.5, 0 is labor's share in innovative costs, and a,, defined in

Appendix B, is a function of parameters and K,. Intuitively, aggregate per-industry

capital is fixed. As I rises, the return to K, rises relative to that of the mobile factor,

L,. Thus, au, /aI = (du, /dw,)(aw, /lI) > 0. The advantage of introducing specific

factors is that. even though production at the firm level exhibits CRS. the representative

industry (or economy-wide aggregate innovative activity) is subject to diminishing

returns. Imitation

The amount of labor employed in imitation is Lc, Kc is the level of capital, and

C is the aggregate level of imitative activity for the representative industry subject to

imitation. Let wc be the return to capital in imitation, aLc be the unit labor requirement.


and aKC be the unit capital requirement (we, aLc and aKC are functions of C). With finns

small, with capital fixed, and with a Cobb-Douglas production function, unit costs are

lc aLC WCaKC ;c.CC' (2.6)

In (2.6), (c 1 -y is labor's share in imitation costs. and ac, defined in Appendix
B, is a function of production function parameters and K(. Hence. auc /3C = (du.

idwc)(9wc /lC) > 0.

2.2.2 Market Equilibrium Product market

Because the total number of industries is of measure one. consumer demand in

each industry is given by (2.3). As noted, quality leaders can capture the market by

charging p = X. A quality leader has a constrained monopoly in equilibrium, and the

monopoly profits are given by

L (X E(t) I l E(t) (2.7)

in which (X-1) is the markup and E(t)/X is quantity demanded in each market. After

imitation occurs, there are two quality leaders who collude. continue to charge price p

= X and divide the market equally. Profits to each are

rc 1 E (2.8)

An important implication of the foregoing discussion is that price is constant over time

and across industries. Collusion turns out to be a fairly convenient method of allowing

for positive expected profits to imitation. Labor market

Labor is homogeneous, the economy has an endowment of L, and the labor

market clears at each moment in time. Labor demand comes from three sources--

production, imitative R&D, and innovative R&D. Since one unit of labor produces one

unit of final product, the demand for labor, at time t, in final goods production equals

E(t) The unit labor requirement for innovation is au, so aLI is the labor demand for

innovative R&D, at each time t, in each industry targeted for innovation. Similarly,

aLcC is the labor demand for imitative R&D, at each time t, in each industry targeted for

imitation. Let 0(t) be the fraction of industries (duopolies) targeted for innovation, and

a(t) be the fraction of industries (monopolies) targeted for imitation. Total R&D labor

demand is 3(t)aaL I oa(t) aLC C. The full employment condition, at time t, is (using (2.5),

(2.6), and the definitions of aLc and aLl in Appendix B)

L E(t) (t)aLlI ()aLC E(t) +e a,(t) ".* yaCa(t) C'l. (2.9)
x A Specific factors

The returns to capital. w, and wc, adjust to ensure that the aggregate amount of

each specific factor (K, K,) is always fully employed. The full-employment conditions


K, aKI P(t) K, K,/I(t) (2.10)

and Kc aKCCa(t) Kc Kc/a(t) (2.11)

2.2.3 Steady State Characteristics

This paper considers a symmetric Nash equilibrium steady state in which

consumer expenditures and the proportion of industries with one quality leader are

assumed to be constant over time. However, since the focus is on the equilibrium

levels of I and C, an equivalent representation of the steady state is developed. The

model is reduced to two equations in I and C. Segerstrom (1991) and Segerstrom and

Davidson (1991) show that innovators will collude with one and only one imitator and

that quality leaders will not collude with previous state-of-the-art producers. This is true


In2>(p ( I') Assumption Al"

In < pA Assumption A2


S> max 3 Assumption A3

In Assumptions A2 and A3, A is the lag before a cheater can be detected violating the

collusive agreement and punished.7

6The denotes a steady-state value.

7In Chapter 2, Assumption Al can be satisfied by choosing the labor endowment
sufficiently small such that I* is small enough to satisfy the inequality. In Chapter 3.
with I' always less than one, Assumption Al will be satisfied if 1n2 > 2pA. This
inequality and Assumption 2 allow a range of A which satisfy the model. Assumption
A3 can be satisfied, for given A and p, by a sufficiently large quality increment. This
is a model that considers large innovations.


The steady state has the same characteristics as Segerstrom (1991): [1]. E and

a are constant over time, by assumption; [2]. r(t) = p which follows from

characteristic [1]. and equation 2.4: [3]. I (or C) is constant across time and industries

targeted for innovation (or imitation), by the assumption of symmetry, the fact that price

is constant across time and from characteristic [1], above: [4]. One quality leader earns

rL, as shown in equation 2.7, and two quality leaders earn re, as shown in equation 2.8:

[5]. There are only two types of industries--those with one leader and those with two

leaders: [6]. In industries with one leader. there is no innovative R&D and previous

quality leaders don't imitate; [7]. In industries with two quality leaders, there is no

imitative R&D and, neither current nor previous leaders innovate. Characteristics [5] -

[7], listed above, are proven in Appendix C. Industrial targeting

Since innovation (or imitation) is governed by a Poisson process. in an interval

of time. dt. an industry becomes an a (0) industry with probability Idt (Cdt). The

proportion of industries becoming a industries in dt is flIdt. The proportion of

industries becoming 3 industries in dt is a Cdt. So, 3 = 1 a and &(t) obeys

&(t) = (1 -a(t))I(t) a(t)C(t) (2.12)

In the steady state, &(t) =0, so aCdt = 3Idt and

aC (1 a)l a L /3 C (2.13)
The number of industries changing from one to two quality leaders) equals the number

of industries changing from two to one leaderss. Zero-profit conditions

Expected discounted collusive profits in the steady state are
x e 17-77
v7 re t"dt le '-dr "c

in which p = r(t) is used. The random time until the next innovation, 7, is exponentially

distributed. Let s be the random time until imitation. The expected discounted benefits

to engaging in imitative activity are

bc = (Ce -c)ve I'ds Cvc
0 (p QC)
Total costs at t are unit cost times C. so the expected discounted costs from engaging in

imitative activity are

ucCe 'sds Ce dt C

recalling that Uc is as given in equation 2.6. Combining these two gives expected profits

from engaging in imitative activity and the zero-profit-in-imitation-condition is

vc t uc (2.14)
The ZPC (zero-profit condition) in innovation is developed in a similar manner.

Innovators, however, have two components to profits. From the point of innovation until

the point of imitation, the innovator earns profits 7L given in equation 2.7. After

imitation, the innovator shares the market with the successful imitator. Because 7, the

time duration of the imitation race, is exponentially distributed, v, the expected

discounted reward from innovating is

X -I
v I j L T.e 'dt e '"vc Ce -dr (TrL c)
o (p, C

Analogous to imitation, the ZPC for innovation is

v u (2.15)
p4C Steady-state equilibrium

The next step is to reduce the model to two equations in C and I and examine the

steady-state equilibrium of the model. To obtain a steady-state labor market condition,

use (2.13) in (2.9):

L C aLl 1LC aL cC (a aLC (2.16)
By substituting for E from (2.8) and for -rc from (2.12), the equilibrium labor

constraint becomes

(2 1)L (aLl aLC)- (I)uc (2.17)

This equation implicitly defines C as a function of I. denoted CL(I). The properties of

CL(I) are derived in appendix D. CL(I) is negatively sloped with a positive intercept.

This equation is graphed in Figure 2.1 (for k4 > 0).


^ (I)


Figure 2.1
The Unique Steady-State Equilibrium


To obtain a steady-state ZPC in R&D. combine (2.7), (2.8), (2.14) and (2.15):
(2(p t I) i C) uc
ut (2 (2.18)
Equation 2.18 defines C,(I), the equilibrium ZPC in R&D. If three conditions--R. R2.

and R3, derived in Appendix D--hold, C,(I) will be positive and positively sloped.

Restriction RI is discussed in section 2.4. Restrictions R2 and R3 are equivalent to the

stability conditions derived in the next section. C,(I) is also graphed in Figure 2.1. and

it's properties are derived in Appendix D. The following proposition summarizes this


Proposition 1

The Nash Equilibrium steady state represented by F in Figure 2.1 exists and is unique.

2.3 Stability and Comparative Statics

Samuelson (1983) explains the duality between stability analysis and meaningful

comparative static results, which he calls the Correspondence Principle. To apple\ this

principle, one postulates an adjustment process, presumably based on rational economic

behavior, whereby the equilibrium condition is achieved. Then, one ascertains under

what conditions, after a small disturbance, this process returns the economy to

equilibrium. This is Samuelson's "stability analysis of the first kind in the small." (1983.

258) Samuelson shows, as I do below in this case, that these stability conditions rule out

perverse comparative statics.

2.3.1 Stability

I will consider only local stability. Recall that unit costs for innovation and

imitation are u1 a I" and uc acC', respectively. At 0 = 4 = 0 (E= 7y = 1), the

model reduces to Segerstrom's (1991) model. At 6 = 0 = 1 (c = y = .5), the model

corresponds in reduced form behavior to Cheng and Tao (1993). First. I demonstrate

that. at 0 = 0 = 0, the model has no stable interior equilibrium. Then, I derive

stability conditions for the general model.

The transitional behavior of the state variable. c(t), will depend on the adjustment

of industry innovative and imitative activity (see equation 2.14) in response to nonzero

profits. To analyze the behavior of this model in the neighborhood of the steady state.

assume that the intensities of industry innovation and imitation obey the following

adjustment rules:

i(t) (v, u,) (2.19)8


((t) F(v. u ,). (2.20)

in which *(0) = F(0) = 0 and I'(), F'(-) > 0. The functions 'I and F convey

continual entry into (or exit from) R&D races whenever expected profits are > (<) 0.

For stability, this behavior must return the model to the steady state, in which C = 0 and

I = 0. after a disturbance. Because this model has specific capital, the adjustment rules

can be thought of as being based on capital movements with adjustment costs in response

to rental differentials, as in Neary (1982). This paper examines local stability, so it is

'The denotes a time derivative.


enough to see that a rental differential would occur (w, w,). By the 'magnification

effect' of Jones (1971), in a three factor model, the change in relative expected benefits

is always trapped between the returns to specific factors. So, for example, a small

increase in v, from F will cause a rental differential in favor of innovative capital.

Substituting into (2.19) from (2.5), (2.7), (2.8), (2.14), (2.15), and (2.16) gives

i(t) = 0 in terms of I and C:
(P. -1) IC 1 _, arl"(P [)(piC)
l)(L (Ceal yacC'' 2(2.21)
2 lC '' 2(p I)iC
Substituting into (2.20) from (2.6). (2.8), (2.14). and (2.16) gives C(t) = 0. which is the

same as (2.17) in the specific Cobb-Douglas form:

(X I) (eIC l" I YacC' ac C'(p I) (2.22)
2 I[ C
The slopes of these two functions are derived below and shown to be less than zero for

all nonnegative 0, ).

When 0 = 6 = 0. C = 0 and I = 0 can be graphed as in Figure 2.2. The values

of the various intercepts are given in Appendix D. But when ,. b are large enough.

as I show below.C > C and i =0 and C = 0 can be graphed as in Figure
dl l, dl c o
2.3. The values of Co and I0 are given in Appendix D. Comparison of Figures 2.2 and

2.3 shows that i = 0 cuts C = 0 from below in Figure 2.2 and from above in Figure

2.3. Using (2.21) and (2.22), it is straightforward to show that, in either case. for given

C, I above i = 0 implies i < 0 and vice versa. Similarly, for given I. C to the right

of C = 0 implies C < 0 and vice versa. These arguments are derived in Appendix E

and are indicated by the arrows in each phase diagram.


I, 12


Figure 2.2
The Unstable Case


I, I

Figure 2.3
The Stable Case


It is apparent that F in Figure 2.2 is not locally stable. To find the stable

equilibria in the case of E = 7 = 1, the extremes of the model are examined. A

disturbance away from F to the northwest will imply C oo. I 0 and then, since all

a industries will be eventually imitated, C 0.' This means that I = C = 0, the no-

growth trap of Aghion and Howitt (1990), is one stable equilibrium. It is stable because

a disturbance away from (0,0) would require I > 0 first. Since only a countable number

of industries would experience innovation at any given point in time, C oo in those

industries and innovative activity would cease. As C 0 to the southeast of F. I -> C

and 3 0. When C = 0, innovators are no longer in danger of imitation, but are

threatened by further innovation. Then v, = rL/(p+I), C = 0, and I = (Tr/ai) p

(which equals I, in Figure 2.2) is the second stable equilibrium when 0 = =0.

In contrast, F in Figure 2.3 is a unique, interior, locally stable equilibrium. So.

for the model to be locally stable, it must be that > in absolute value in the
dl i-_o dI 0I
neighborhood of F. By differentiating (2.21) and (2.22) and comparing these slopes at

the steady-state equilibrium, it is possible to derive the restrictions on 0 and 4 such that

local stability occurs. Differentiating (2.21) and (2.22) gives

0(p+l)al" 1(p C) + acC 1!'l
dC (2(p +1)C)j (2.23)
dl aI(p (p +)(p 21)+

(2(p 1) C)2

"As C increases and I decreases, a falls and ever fewer industries are subject to
innovation and this process accelerates over time. As a -* 0, C oo. Because each
industry is infinitesimal, it is possible to have C -*oo in an individual industry even if
L is finite.


di c=O

X + acC'
IY + (ac.C"^ (p l)


(Notice that (2.23) and (2.24) are negative.) In (2.23) and (2.24),

X = -1) C2 (Eal"
2 (I+C)2

- yacC6)

IC 0Eal"

Y ) (Ea yacC"') IC ya C6'
2 ( C)2 ICC C

Stability can be assured if

(O(p+D)al-I(p+C)) a acC'O-C'
> aC'
2(pI -1) C

acC(- > a1l(pe2I)
(2 a. ^ I )
(2( p 1) QC)



with one or both holding with strict inequality. By substituting from (2.18) for (p+C)/

(2(p+I)+C) and cancelling terms, (2.25) reduces to 0 :2 21 /(2(p+I)+C), which holds


0 2 I or <- .


By rearranging (2.26),

a > a1 c C
a, a" ( tp -C)J a
and since the bracketed term is less than one. and the term in parentheses is at most V/

by (RI), given on page 35 below, then,


4 '/2 ory <- (SC2)

(SC1) and (SC2) are sufficient conditions for stability so long as at least one holds with

strict inequality. These require sufficient diminishing returns to innovation and imitation.

Why are diminishing returns so important? Examination of the ZPCs. (2.14) and

(2.15), provides an answer. In a partial equilibrium sense, in any industry where profits

are positive, it must be that free entry into that market drives them to zero. Otherwise.

entry continues unabated, and the ZPC is never satisfied. In this model, free entry does

not directly lower the expected benefits so it must raise costs. Suppose that a disturbance

causes v, > u,. If u, is constant, the only way to reequate (2.14) is for C to rise since

av,/aC < 0. Operating through the labor constraint. I falls. If u, increases only slowly

with I then v, might rise faster than u, as I rises, widening the gap. This is because I

rising makes vc fall so that vc < uc. C falling in response (by a relatively larger amount

the less ui rises with C) will increase v,, possibly more rapidly than u,. Profits would

increase and equilibrium would not be reestablished. If there are sufficient diminishing

returns to scale in R&D (i.e., (SC1) and (SC2) hold), then u, rises more rapidly than v,

as I rises and this reequates expected profits to zero.

2.3.2 Comparative Statics

It follows directly from the stability analysis that the comparative static results

depend on whether (SCI) and (SC2) hold. Suppose the government gives a lump sum

per unit subsidy to innovative R&D. It is not difficult to show that a small subsidy will

shift I up in Figures 2.2 and 2.3 resulting in a lower I and higher C in Figure 2.2 and

a higher I and lower C in Figure 2.3. A subsidy to C will also shift C out, increasing


C and decreasing I if the model is locally stable. Intuitively, perverse comparative static

results in the neighborhood of F are eliminated when the model becomes locally stable.

This is the Correspondence Principle. Comparative static results are derived in Appendix

F. The discussion in this section leads to the following proposition:

Proposition 2

When there are sufficient instantaneous decreasing returns to each R&D activity

((SC1) and (SC2) hold), the model is stable and the comparative static results of subsidies

to R&D activity are as e.\pecteld: a subsidy to innovative activity increases I, and a

subsidy to imitative activity increases C. Wie~ n there are not sufficient instantaneous

decreasing returns to each R&D activity ((SC1) and ((SC2) don't hold), the model is

unstable, and the comparative static results are reversed.

2.4 Restrictions And An Example

2.4 1 Restrictioins

Here I discuss the various parameter restrictions. It is shown in Segerstrom

(1991) that X large enough and L small enough to satisfy Assumptions A1-A3 are

required. In the previous section, 0 > 1 and 6 > 2 were shown to be sufficient for

stability. There is one other inequality which must hold in the steady state for a well-

behaved model. This restriction, (RI), must hold for C > 0, I > 0 (See Appendix D):

2> a > (RI)
acC "


This restriction implies that the model requires partial diffusion of product

technology from innovators to imitators. It also limits the cost advantage that imitation

has, relative to innovation. One way to ensure that (RI) holds is to assume that specific

capital is mobile in the long run and that the economy is in long-run equilibrium at F in

Figure 2.1. The return to capital will then be equalized across sectors, and there will

be a relationship between the 'price' or expected benefit ratio, the wage/return to capital

ratio, and the capital/labor ratios of the two activities, as described by the Samuelson

diagram in Figure 2.4. Assume that L is the total labor available to R&D in the steady

state and that innovation is capital intensive relative to imitation (y > E). Then,



K\L (K\L),(

1 \w



V( \V1

V(.\VI = U(,\UI

Figure 2.4
The Range of uc\u,

Kr 37
IuI Ac L1
uc e Ai Kc Y


where Ac and A, are the general coefficients of the Cobb-Douglas production functions

for imitation and innovation, respectively, defined in Appendix B. By examination of

Figure 2.4, it should be apparent that, for an appropriate choice of e, y, A,, and Ac

(which position the two functions in the top quadrant), choosing K. the total

economy endowment of capital, for given L (already restricted above), can limit the

range of u,\Uc (EF in Fig. 2.4).

2.4.2 Example

It remains to show an example in which (RI) holds and the model is well-

behaved. Let L = 1, K = 2, e = /4, y = '. Ac = 2, A, = 1, X = 4, and p = .05.

Then 0 = 3, satisfying (SC1) and
Cobb-Douglas functions of Appendix B, the range of w, = w, in the long run is (1. 1 /2z)

the range of u, is then (1.76. 2.378), and the range of uc is (.95, 1.238). Then the range

of ui/uc is (1.857. 1.921), satisfying (RI). Using (2.17) and (2.18), C' = 1.93 and I'

= .83 when w, = w = 1, and C* = 1.94 and I* = .94 when w, =wc=11/2. This is

one example where all restrictions of the model are satisfied.

2.5 Conclusion

I have used Samuelson's Correspondence Principle to develop stability conditions

for a generalized version of the Neo-Schumpeterian growth model of Segerstrom (1991).


Innovation and imitation are endogenously determined in a dynamic. zero-profit, general

equilibrium model of growth in consumer utility through quality improvements. Each

R&D activity uses labor and specific capital. Standard adjustment mechanisms, supported

in principle by the work of Neary (1982), are used in the stability analysis. I show that

sufficient instantaneous decreasing returns to scale in R&D are required for a well-

behaved model in which the comparative static results are reasonable.

The implication for future work is that the inclusion of separate R&D sectors in

a dynamic general equilibrium model with levels of R&D activity determined by free

entry and zero-profit conditions imposes restrictions on the structure of the model. The

mathematical sophistication of Segerstrom's model disguises the stability problem. but

an appeal to Samuelson's analysis clarifies the issues.


3.1 Introduction

A photograph snapped at a fashion show in Milan can be faxed
overnight to a Hong Kong factory, which can turn out a sample in
a manner of hours. That sample can be fedexed back to a New
York showroom the next day.

Wall Street Journal 8-8-94

Imitation of new products or processes is an increasingly important avenue of

technology transfer in the global marketplace. In the U.S., it is estimated that sixty

percent of patented innovations are imitated within four years.' Furthermore. among

advanced countries, the rate of international technology transfer through imitation

depends on R&D investment.: Finally, technology transfers flow in all directions among

'Mansfield et al. (1981), pg. 913. This paper investigates, through case studies, the
magnitude and determinants of imitation costs and the relationship of these costs to
innovation costs, the imitation time lag, patents, and entry.

2Mansfield et al. (1982), pg. 35. Based on data from 37 innovations in the plastics.
semiconductors, and pharmaceutical industries, this study also concludes that imitation
lags appear to be decreasing over time.


advanced countries.3 Japan spends resources to copy U.S. technology in semiconductors

and automobiles, but U.S. companies also try (with limited success) to transfer Japanese

technology (i.e. quality circles) to the U.S.4

Several endogenous growth models include various aspects of the complex

dynamics of imitation. First, Segerstrom, Anant and Dinopoulos (1990) and Dinopoulos.

Oehmke and Segerstrom (1993) model imitation as an exogenous, certain and costless

activity. These studies explore the effects of changes in the imitation lag on innovation

and growth. Second. Grossman and Helpman (1991a) develop a model of North South

trade in which the South engages in endogenous imitation based on expected profits from

lower manufacturing costs, which result in a lower wage. None of the models mentioned

above endogenizes imitation among advanced countries with identical wages. Nor do any

generate multidirectional patterns of endogenous international technology transfer.

To that end, this chapter develops a two-country model of growth based on the

introduction of new products of higher quality. This model is closely related to that of

Chapter 2. Endogenous innovation and endogenous imitation influence both consumer

utility and trading patterns. To simplify the analysis, I assume that there is only one

factor of production, labor. Instantaneous diminishing returns to R&D. essential for

'See Eaton and Kortum (1994) and Coe and Helpman (1993). The first study, using
data on patents, productivity, and research in five leading research economies, reports
that, for each country, more than 50 percent of productivity growth is attributable to
foreign technology. The second study, using data on 22 OECD countries, finds that
international R&D spillovers to trading partners accounts for about one quarter of the
total social return to the R&D investment of the seven largest OECD economies.

4Dinopoulos and Kreinin (1994) report that U.S. companies spent $950 billion, in the
period 1983-1993, in an attempt to implement Japanese management techniques (p.2).


stability, are achieved through specific functional forms. A new element is the important

role assumed by imitative activity in the ongoing global growth process. Imitative

activity diffuses leading edge technology and keeps the industry competitive in R&D.

The model is used to analyze the effects of differences in relative labor endowments on

trading patterns and technology transfer. This analysis is conducted in an integrated

global economy in which factor price equalization (FPE) prevails.

The results of the analysis can be summarized as follows. A unique, stable,

integrated equilibrium is found to exist (Proposition 3), in which both innovation and

imitation contribute to growth and welfare (Proposition 4). An increase in the world

labor endowment increases the rates of innovation, imitation, and growth: a world

subsidy to innovation (or imitation), increases the rate of innovation (or imitation)

(Proposition 5). For a large set of endowments, the integrated equilibrium can be

replicated, under factor price equalization, by trade in final goods, without direct foreign

investment (DFI) or trade in R&D services (Proposition 6). Stochastic trade patterns

with two-way international technology transfer and product cycles are generated for a

wide range of endowments (Proposition 7).

The following pages set out the model and establish the global equilibrium

(Section 3.2), examine welfare and growth (Section 3.3), discuss international technology

transfer and trade patterns (Section 3.4); and look at the conclusions to be drawn from

the analysis and elaborate implications for future research (Section 3.5).

3.2 World Economy

3.2.1 Overview

A representative agent maximizes utility over time and over a continuum of final

goods subject to stochastic quality increments of fixed amount. Consumer sa% ings are

channeled through an asset market to finns investing in R&D. In each industry. firms

'buy' a probability of winning the race to discover the next (or copy the latest) quality

level by engaging in costly innovative (or imitative) activity. There is free entry into

each innovation (or imitation) race. The successful innovator captures the market

through limit pricing and enjoys temporary monopoly profits until its product quality is

imitated. Successful imitators duplicate the industry leader's product quality and collude

with the quality leader to obtain temporary duopoly profits until the next innovation

occurs in that industry.

Production of final goods exhibits CRS in labor, but requires knowledge of the

current state of the art. There are instantaneous diminishing returns to aggregate industry

R&D activity. Put differently, the probability of an innovation (or imitation) occurring

is concave and increasing in the amount of resources devoted to innovative (or imitative)

activity. Unit labor requirements in each R&D activity are endogenously determined.

In the steady state, world expenditures, levels of innovative and imitative activity

per industry, and the percentage of monopoly industries are constant over time. Each

industry is first targeted for innovation, and then, for imitative, races, so market

structure fluctuates between monopoly and duopoly in stochastic cycles. The following


subsections describe consumer behavior, the product markets, R&D races, the labor

market, and the existence of the integrated equilibrium.

3.2.2 Consumer Behavior

The representative world consumer maximizes an intertemporal utility function

identical to that in Chapter 2. with a CDP instantaneous utility function. The usual static

maximization problem yields

dh, (6) E(t) (3.1)
as world industry demand at time t. where h =_ h,(w) is the highest quality available at

time t in industry w. E(t) is instantaneous expenditure, and Phi() is the price of good h

at time t

is the condition of intertemporal maximization, r(t) is the instantaneous interest rate

which clears the asset market continuously, and p is the subjective discount rate.

3.2.3 Product Markets

The current quality leader captures the market with a limit price determined by

its degree of quality advantage, which is equal to h, the quality increment over the

previous quality. If labor is the numeraire, p = X in each industry at all times. A

successful innovator becomes the sole producer in that industry and can earn monopoly

profits of

Trr E(t) i E(t) (3.3)

where (X-l) is the markup and E(t)/X is industry demand. Industries in which there is

a single producer are denoted as a-industries. When this new quality is imitated, the


winner of that race can collude with the current leader. They charge p = X, split the

market, and each earn

'c l1 2 (3.4)
I I)E(t) (3.4)

Industries with two producers are denoted as 3-industries.

3.2.4 Innovative R&D

Innovative R&D activity occurs only in duopoly, 0. industries in which diffusion

of the current state-of-the-art technology through imitation is complete.5 By engaging in

i units of innovative activity in industry o. a firm buys the probability idt of successfully

carrying out the next innovation in the industry in interval dt. The arrival rate of

innovations is a Poisson process, and the time duration of each innovation race is

exponentially distributed. Aggregate industry innovative activity, I. is the mean rate of

occurrence of innovations. Idt is the probability that if the innovation hasn't occurred

by time t, it will by time t+dt.

The firm's level of innovative activity can be related to the amount of labor it

i 1
(a, f bL, )
The variable 1, is the amount of labor hired by a firm engaged in innovation; L, is

aggregate industry employment in innovation; a, is the minimum unit labor costs of

innovative R&D. The variable b, measures the degree to which the level of industry

innovative activity lowers the individual firm's labor productivity.

5It is assumed that the whole industry (not just the monopolist) must be on the
technology frontier before it can engage in innovation. This is discussed in more detail


Aggregate innovative activity in each industry targeted for innovation is given by
(a, bLt)
The aggregate industry probability of success is a concave function of industry labor

employed in innovation. A possible source of instantaneous diminishing returns to

innovative R&D is a negative externality associated with rising industry innovative

activity. The increased possibility of parallel research programs reduces the

effectiveness of additional R&D activity in quickening the pace of innovation.6

Substituting from (3.5) for L,, unit labor requirements (and unit costs when w= 1) for

innovation are
LI a
III aI b ,iLI (3.6)
I ( b11)

Innovative activity is subject to diminishing returns at the industry level, but individual

firms regard costs as constant since they take L, and I as given.

3.2.5 Imitative R&D

Imitative activity plays an important implicit role in this model. Through an

exogenous effect occurring at the end of each R&D race. the imitation process lowers

the minimum unit costs of engaging in the next innovation race. This may occur because

of experience gained in conducting R&D. Imitative activity is modeled in a parallel

'Stokey (1992) makes this same argument for instantaneous diminishing returns to

71t is assumed that these effects are large enough that innovation never occurs in an
a-industry. In monopoly, a, industries, minimum unit labor costs are assumed to be aD,,
where aID > a,. We can assume that aD -C oo. Since this is a model which considers
large innovations, as is pointed out below, this is like saying that at the time of the
introduction of black and white TV, color was not an immediate possibility.


fashion to innovative activity. By engaging in c units of imitative activity in an industry

targeted for imitation, a firm buys the probability cdt of successfully copying the current

state-of-the-art quality in that industry in interval dt. The arrival rate of imitations is a

Poisson process and the time duration of each imitation race is exponentially distributed.

Aggregate industry imitative activity, C, is the mean rate of occurrence of imitations.

Cdt is the probability that the imitation occurs in interval dt.

Aggregate imitative activity in each industry targeted for imitation is
C c (3.7)
(ac bcLc)
The term Lc is aggregate industry employment in imitation: ac is the minimum unit labor

costs of imitative R&D; be measures the degree to which the level of industry imitative

activity lowers the individual firm's labor productivity. The aggregate industry

probability of success is a concave function of industry labor employed in imitation. The

source of diminishing returns to imitative R&D is also a negative externality associated

with rising industry imitative activity. Substituting from (3.7) for LC., unit labor

requirements (and unit costs when w= 1) for imitation are
Lc ac
uc ac ( bcLC (3.8)
C (I bcC)
Imitative activity is subject to diminishing returns at the industry level, but individual

finns view unit costs as constant by taking L, and C as given.

3.2.6 Labor Market

The competitive labor market clears at all times. The full-employment condition

L tiU1(t)l tcua(t)C (3.9)


The term L is the total world endowment of labor; E/X is the labor required to produce

final goods; u, and uc are the labor requirements in innovation and imitation respectively,

as defined in (3.6) and (3.8). The term 3 is the proportion of industries undergoing

innovation, and I is the per industry level of innovation. Hence, 0I is world innovative

activity. Also, because a is the proportion of industries undergoing imitation, and C is

the per industry level of imitative activity. aC is world imitative activity.

3.2.7 Industrial Targeting

The evolution of industries with one quality leader is

&(t) = (1 -ca(t))[l ((t)C (3.10)

When d(t) 0, as it does in the steady state,
a = 3 (3.11)
liC IC
These equations are identical to (2.12) and (2.13), in section

3.2.8 Steady-State Equilibrium

The steady state is assumed to be one in which world consumer expenditure

flows. E, and the proportion of industries with one quality leader, a, are constant over

time, and I (or C) is constant across all f (or a) industries and time. Under these

assumptions, a symmetric Nash equilibrium steady state exists with the following

characteristics: the instantaneous interest rate equals the subjective discount rate (r(t)

= p). No R&D is conducted by current monopolists or duopolists. Only duopoly

(/) industries are targeted for innovation races, and only monopoly (a) industries are

targeted for imitation. Thus, I (or C) is zero in all a (or 3) industries. There are only

two types of market structure--monopoly and duopoly. This is because, due to parameter


restrictions made for ease of analysis, collusion is only supportable between the innovator

and one imitator. There is one winner of any given imitation race. Each industry

follows a stochastic sequence of alternating periods of innovation followed by imitation.

as it climbs up its quality ladder.

There are two types of intraindustry intertemporal R&D spillovers in the steady

state. There are endogenous spillovers from innovation to imitation. In equilibrium, unit

costs of imitation are lower than unit costs of innovation. The same probability of

success in interval dt can be purchased for less in an imitation race. This type of

spillover can arise when innovators cannot appropriate all of the knowledge associated

with their product. Some knowledge may be embodied in the product, for example.

The second (exogenous) type of intertemporal R&D spillover, from one product

cycle to the next, is captured by the assumption that the minimum unit costs of

innovation, a,, are constant over time, even though each innovation is more valuable than

the previous one. In models with innovation only. this characteristic of the model is

explained as the result of exogenous spillovers of knowledge, whereby current

competitors in an innovation race can effortlessly acquire all information pertinent to the

previous innovation, which assists their efforts in the current race. This interpretation

doesn't make sense, however, in a model in which an industry makes imitative R&D

expenditures expressly to learn current technology.

In fact. though still exogenous, these spillovers can be interpreted as working

through the imitation process. The imitation process diffuses the current state-of-the-art

throughout the industry, and increases industry experience in R&D. If the second effect


is large, as is assumed, even the industry leader will not engage in innovative activity

prior to imitation. So, it may be that there are spillovers of knowledge from previous

innovations, but these are not completely disembodied. They are associated with

imitative R&D activity and can be interpreted as a by-product of the competitive race for

collusive profits. Assume that the industry in general moves close enough to the

technology frontier and gains enough R&D experience, as a consequence of the imitation

race, to engage in the next innovation race at minimum unit costs a,. By assumption, the

costs of carrying out the next innovation are prohibitively high until after imitation of the

current quality has occurred and the information obtained has substantially increased the

productivity of labor engaged in the next innovation race.

Let aID denote the minimum unit costs (labor requirements) of innovation in an

a-industry. The assumption is that
3(, a )L
aID >3( Assumption A4
Assumption A4 states that unit labor requirements for innovation in an a-industry are so

high, relative to the world endowment of labor, that innovative activity never occurs in

an a-industry. The unit costs of the innovation race to discover the j + 1h quality are aD

during the monopoly stage of quality j, but fall to a, as a result of experience gained in

R&D activity associated with the duplication of quality j. These effects are exogenous

and symmetric across industries. This characteristic leads to the cyclical nature of the

market structure in which, in each industry, each innovation must be imitated before

research can begin to discovery its replacement.


Under free entry, zero-profit conditions (ZPC), which govern the level of

innovation and imitation, equate expected discounted rewards to expected costs. The

ZPC's in each industry are, for innovation.
7I"L C vC a,
v,- u (3.12)
p 4 C 1 -blI
and for imitation,

vc = uc a. (3.13)
(pl) 1 b C
Part of v,, the expected discounted reward to innovation, are dominant profit flows, rL.

The other part of v, represents the expected value of collusive profit flows. Expected

discounted benefits to imitation, vt, are collusive profits discounted by the instantaneous

interest rate, r(t) = p, plus the probability of subsequent innovation in that industry. I.

which represents the probability that the flow of profits will stop. v, also represents

expected discounted benefits to the innovator after imitation occurs. Since C is the mean

rate of occurrence of imitations, Cv, is the expected value of collusive profit flows to the

innovator. All benefit streams to the innovator are discounted by the subjective discount

rate and the threat of imitation. By no arbitrage conditions in the asset market, v, and

vc are also the finn values of successful innovators and imitators. '

The model can be reduced to the endo2enous determination of I' and C' (*

denotes a steady state alue). How these change over time. out of the steady state.

determine how E(t) and a(t) evolve over time. In the steady state. I. C. E and a are

constant. Assume that

I T'(v, u,) (3.14)

'See Dinopoulos (1994).

C P (vc uc) (3.15)

where V' and c' are greater than zero and 'I(O) = D(0) = 0 (looking at (3.13), it is

apparent that I = 0 and C = 0 imply = 0 ). Substituting into (3.14) from (3.3),

(3.4), (3.6), (3.8), (3.9), (3.11), (3.12), and (3.13): and letting I = 0. as in the steady


(-1) IC a ac (P'I)(p C)a,
L ( c (3.16)
2 I+C 1 -bl I bcC (2(p I) C)( -bl) )1)
Substituting into (3.15) from (3.4), (3.6), (3.8), (3.9), (3.11), and (3.13); and letting

(I -1) IC a, ac ( ac
L + (p1l) (3.17)
SIC bl I bcC It bcC
Finally, combining (3.3), (3.4), (3.12), and (3.13) gives a steady-state zero-profit

at 2(p1) +C ac
(l-blI) (p+C) (1 -bC)
Note that, using (3.6) and (3.8), u,,uc is always greater than one in the steady state by

(3.18). So, there are spillovers from innovation to imitation, the magnitude of which are

endogenously determined. These R&D spillovers must exist for imitation to be profitable

relative to innovation since gross returns to innovation are greater.

Equations (3.16), (3.17) and (3.18) can be graphed as in Figure 3.1 where I, <

Io and C, > Co if

2ap > (. I)L > max iap 1 Assumption A5

a, /ac 2, Assumption A6

b > max a I and bc> Assumption A7
p p



C1 T

/' ---- C=0

0 I 1

Figure 3.1

Assumption A5 requires that the world labor force be large enough to support innovation

but not too large. Assumption A6 is consistent with innovation being more expensive

than imitation. Assumption A7 gives the stability conditions which guarantee that =

0 cuts C = 0 from above. Given Assumptions Al A7.

Proposition 3

The Nash equilibrium steady state represented in Figure 3.1 exists and is unique

and stable.

Proof: See Appendix D for the properties of (3.16). (3.17), and (3.18), which, when

graphed in Figure 3.1, shows F to be a unique equilibrium. F is shown to be a stable

equilibrium in Appendix E.

3.3 Welfare and Comparative Statics

Appendix G shows that the world representative agent enjoys a certain and

continuous growth rate in steady-state expected utility of
I 'C 'In0 1\
"g I In (3.19)
1l+C (1/1) (/C)
and steady-state expected discounted welfare of

U In -1 l (3.20)
Both innovation and imitation influence growth, and both growth and current

expenditures affect welfare. Equation 3.20 is not surprising in a dynamic model.

Equation 3.19, however, is unusual in that imitation contributes positively to growth for

a given level of I, as is clear from the discussion of Assumption A4. Each quality level

must go through a period of innovation followed by imitation. In equation (3.19), 1/I

and 1iC are the expected durations of innovation and imitation races respectively. I/I

+ 1/C is, therefore, the expected duration of R&D activity associated with each quality

level which must occur before the next cycle can begin.

Appendix G shows that, given Assumption A4 and

b, = 2b Assumption A8

the following is true:

Proposition 4

The t elfare maximizing levels of innovation and imitation are positive.


Assumption A8 is probably more restrictive than necessary, but simplifies the

algebra. Nethertheless, it captures the notion that innovation is more difficult than

imitation. Proposition 4 occurs because diffusion through imitation is a necessary part

of the ongoing growth. This is an interesting result because it embodies a positive role

for imitation that operates through the production side. Any positive effects of imitation

are usually thought to occur because of either product differentiation or increased


Before leaving the discussion of growth and welfare, and as a prelude to the

discussion of trade patterns, it is useful to note the effect of an increase in the size of the

economy on the rate of growth and welfare. An increase in L shifts both curves out

in Figure 3.1 but leaves Czpc unchanged (see (3.16), (3.17) and (3.18)). Therefore. I*

and C* increase, which increases the growth rate for a given level of expenditure. World

welfare rises. This demonstrates the economies of scale characteristic of these models

when R&D expenditures are spread over larger markets. The potential for gains from

integration exists. The comparative static results of subsidies to innovation and imitation

are also given in Proposition 5:

Proposition 5

(i) An increase in the world labor endowment increases innovative activity, imitative

activity, growth and welfare.

"See Dinopoulos (1992) and Davidson and Segerstrom (1994) for examples of these
two effects. There is a substantial partial equilibrium literature that studies the
contribution of imitation to diffusion of technology. See Baldwin and Scott (1987) for
a survey of this literature and Cohen and Levinthal (1989) for a general equilibrium
treatment of this effect.


(ii) An increase in a per unit subsidy to innovative activity increases innovative activity.

(iii) An increase in a per unit subsidy to imitative activity increases imitative activity.

Proof: (i) is discussed above. (ii) and (iii) are discussed in Appendix F.

3.4 Trade and Technology Transfer

The technique used to analyze trade patterns is the integrated equilibrium

approach employed by Helpman and Knigman (1993). The integrated equilibrium.

established in Proposition I and indicated by F in Figure 3.1. represents the world

allocation of resources when labor is perfectly mobile. This section analyzes trade

patterns that can occur when free trade, between two countries with immobile labor.

replicates the integrated equilibrium and the wage rate is equalized. International

technology transfer, through imitation, influences these trade patterns. The extent of

these technology transfers is governed by relative national labor endowments. The first

subsection explores the assumptions that shape the trading environment and derives the

labor constraints for each country and the trade balance. The next subsection looks at

the conditions under which the wage rate is equal across countries. Finally, the trade and

technology transfer patterns that can occur in the replicated integrated equilibrium are


3.4.1 Assumptions/Trading Framework

The following Assumptions are made: A9 Technology cannot be transferred

costlessly between firms or across borders. A10 Labor is not internationally mobile.


All Financial capital is internationally mobile. A12 Each country targets all a (or 3)

industries equally for imitation (or innovation). A13 Each country's share of assets

equals its share of world labor. A14 The percentage of monopoly and duopoly

industries in each country is constant over time in the steady state. A15 Each country's

expenditures are constant across time in the steady state. A16 R&D and final goods

production technologies are identical across countries as is the magnitude of quality

increments. A17 Trade is frictionless and unimpeded. A18 Each country's

representative agent has the same homothetic CDP utility.

Assumption A9 is consistent with the evidence. O DFI occurs when foreign firms

conduct either innovative or imitative R&D in the home country or when home fimns

conduct R&D in foreign countries, but only imitative R&D represents the costly transfer

of technology. Since R&D technologies are identical across countries and market share

and profits are independent of both country of production and country of ownership.

there is no motive for DFI when the wage rate is equalized. Thus. it is assumed that

there are no multinationals. Licensing, one firm selling the rights of production to

another, is possible but would involve some learning expenditures of uncertain length and

effectiveness. Licensing is, therefore, compatible with costly imitation. but is not

considered. Trade in R&D services is assumed not to occur, either through DFI or

licensing. Furthermore, there are no (intermediate or capital) traded goods that might

u"See Baldwin and Scott (1987), Ch. 4. which surveys the theoretical literature and
empirical evidence on the diffusion of innovations. A general conclusion is that "the
transfer of technical information is rarely, if ever. costless: and it may be risky as well"
(p. 116).


embody technology. Therefore, each country must invest its own resources in and win

R&D races to participate in final goods production.

The labor constraints can now be constructed. Let subscripts H and F denote

Home and Foreign variables. Let a denote Home's proportion of the labor endowment.


LH 1 L (3.21)

Define CH as the proportion of dominant firms in Home, 3H as the proportion of

duopolies based totally in Home, and 3 as the proportion of duopolies in which one

duopolist resides in each country. Let s be the fraction of final goods manufactured in

Home. Then

s = aH 3H 3/2 (3.22)

The Home and Foreign labor constraints are, considering Assumption A12 and using

Equation 3.22,

LH /3LIH LCH (3.23)


LF (1-s)- ,3LIF aLF (3.24)

where L4H + LF = L, is total labor employed in innovation, and LCH + LpC = L, is

total labor employed in imitation.

Consider Home's share of manufacturing. Assumptions A12 and A14 imply that

aH 3IHdt aH Cdt 0 This, together with (3.11), implies that
aH H (3.25)
I'+C I'
The same assumptions imply that f"H aCH H H 1H I 0 or

C l o
/H CH IH (3.26)
C' I'
Since / /H / F = 0 it follows that / aCH H+ OHCF 3I' 0 or
F p- aH (3.27)
I' I'
All this implies that

H 2/2 H,-C' 0 (3.28)

These equations are easily interpreted. Recall that there is no trade in R&D services so

that all production within a country is due to R&D carried out in that country. Then s

and (1-s) are determined by the relative amounts of R&D done in each country. For

example, if Home does one half of the world innovative R&D. by the Law of Large

Numbers, it will win one half of innovation races and, in the steady state, will have one

half of all dominant firms. If Home also does one half of all world imitative R&D. it

will have one half of all duopoly industry firms. Home would then have one half of all

manufacturing production.

Turn next to the trade balance. Since each consumer is completely diversified,

each will own a share of each successful firm in the exact proportion to her share of

world assets. Given international financial capital mobility, consumer intertemporal

maximization, and EH EF E 0 then, r = rH = r = p in the steady state. Let

Y = YH + YF be the total value of world assets, in the steady state, made up of assets

held by the Home and Foreign agents respectively. Let VH be the total value of Home



VH H V H I (13 /2)Vc


Then, Y = V = VH + VF = av, + i3vc. Y must be constant by Assumption A15.

Since E. I, and C are constant, v, and v, are also constant (See (3.3), (3.4), (3.12),

(3.13)). Since & 6H = 0 by Assumption A14, VH and VF are constant. Note

that, by Assumption A13, Home's share of world assets is equal to its share of labor.

Then. YH = aY = aVH + oVF and Y, = (1-U)VH + (1-o)VF. Since there is no trade

in assets, the current account must balance:
s- (1-s)- pVF (1 O)pVH 0 (3.30)
The first term is Home exports: the second is Home imports. Their difference represents

the merchandise trade balance. The third term. Home's interest receipts, less the last

term. Home's interest payments, is the service account.

3.4.2 Factor Price Equalization Set

The FPE set, or set of relative national labor endowments which can reproduce

the integrated equilibrium, can now be derived. In this model, FPE will always hold if

both countries engage in R&D activity. Because of integration of final goods markets

(which implies a single global innovation race with a single winner) and the nature of the

externality associated with R&D activity, world labor employed in innovation (or

imitation) determines firm and industry unit labor requirements at home and abroad."

Unit labor requirements are endogenous, but are always equal across countries in each

"If a different, country-specific, source of instantaneous diminishing returns to R&D
(such as immobile specific factors) is assumed, then a wage differential can occur which,
if large enough, will lead to a collapse of the collusive equilibrium. The model would
then revert to a North-South model.


R&D activity, and also in final goods production, by Assumption A16. Countries cannot

specialize in production, however, without incurring R&D expenses, by Assumption A9.

Because specialization is impossible, the wages in each country must be equal.

Suppose that the wage in Home. wH, is higher than the wage in Foreign. WF. Unit costs

of both R&D activities will be greater at Home (u,'WH > u,'WF ,. ucWH > uCwWF).-

Similarly, since marginal costs of final goods production are higher at Home (wH > WF),

profits and expected discounted benefits to either R&D activity will be lower at Home.

By financial capital mobility, funds would flow to Foreign R&D races, bidding up wages

there and lowering wages at Home. Labor mobility within each country, and trade and

financial capital mobility between countries. equalizes wages. Consequently, as long as

each country has a sufficient relative endowment of labor to acquire production through

innovative R&D at u,', imitative R&D at uc'. or both, the integrated equilibrium can be

reproduced by trade under FPE.

Defining the FPE set is a matter of determining what the minimum share of labor

is for each country to men.age in R&D and the associated production. Because each

country is assumed to engage in innovation in all 3 industries, and imitation in all a

industries, and because each country must engage in production of final goods for every

race it wins, there is a minimum labor endowment below which the country cannot carry

out these activities. For any endowment point that allocates a share of labor less than

2u1* and ut' are the global integrated equilibrium steady state unit labor requirements
in innovation and imitation respectively.


this minimum to either country, the integrated equilibrium will not be reproduced by

trade under FPE.

The FPE set is represented graphically in Figure 3.2. Let the total length of the

line be L. The Home country's share of labor increases as the endowment point moves

to the right. The Foreign country's share increases as it moves to the left. The point

labelled L, represents the endowment point for which Home's share of labor is at the

minimum necessary to sustain production through innovation or imitation, whichever

requires less labor at the margin in the integrated equilibrium. The point labelled LF


-0 FPE L- -
--------- FPE -----------
o I



Figure 3.2
Factor Price Equalization Set

represents the same for the Foreign country. Hence, in the regions 0 LH and

L, L FPE cannot be maintained by trade under the assumptions outlined above.


In the first region, Home is too small: in the second. Foreign is too small. 3 Therefore,

LH LF is the set of endowment points for which both countries are large enough

to conduct R&D at u,* and uc, and carry out the associated production. FPE must occur

through trade, and the integrated equilibrium will be reproduced. The results of this

section are summarized in Proposition 6:

Proposition 6

If the distribution of labor endowments lies in the region L, L, in Figure

3.2. the integrated equilibrium. represented by F in Figure 3. 1, can be achieved by

balanced trade, between similar countries, in which there is no DFI or trade in R&D


3.4.3 Trade Patterns

Having defined the FPE set, it is now convenient to turn to the characterization

of trade patterns that can occur when the endowment point is in the FPE set. It is

possible to get an expression relating Home's endowment of labor to Home's labor

allocations across activities in a way consistent with the allocations in the integrated

equilibrium. Assume that L the total world endowment of labor, satisfies Assumption

A6, and the endowment point is in the FPE set. Relaxing the normalization on labor so

"These minimum endowment points are derived in the Appendix H. It should be
noted that, because each industry is of measure zero, if Assumption A13 is relaxed so
that a country can target a selected set of industries for R&D, FPE will occur for all
possible endowments. However, almost any alternative to Assumption A13 will render
the model either more complicated or less interesting. A relaxation of Assumption A0.,
so that multinationals can costlessly transfer production abroad, will also assure FPE for
all possible endowment points, but that would be contrary to the evidence. Neither of
these points will be pursued further because trade patterns are only analyzed within the
FPE set.

that demand for labor in Home production is per industry; using (3.3), (3.4),
(3.12) and (3.13) in (3.23) and (3.24); solving for wH and wF; and setting them equal

gives, after some manipulation,

(sL LH) (s-o)L /3(sLI LIH) Y'(sLc LCH) (3.31)

This equation summarizes the patterns of labor employment at Home that are consistent

with FPE. If the world economy can be represented by an integrated equilibrium in

which each country faces the same prices and techniques of production, this equation

must be satisfied. The special case. discussed below, will make it clear that this set is

not empty. From (3.31) alone, under factor price equalization, there are multiple

possible allocations of labor across activities in each country. Therefore, the pattern of

trade is indeterminant.

Nethertheless, additional assumptions will uncover the rich patterns of trade

possible in this model. Refer back to Figure 3.2. LH is defined as the minimum

labor endowment point below which the home country is too small to conduct both
innovation and imitation, and the associated production of final goods. LF is

defined in a similar fashion for the Foreign country. If the endowment point falls within

LH L both countries can engage in both types of R&D activity and the

associated production of final goods.

MM M Al s
Assume that the endowment point is in the region LH L Also assume

symmetric labor activity. The two countries employ labor in each activity equal, in

proportion, to their relative labor supply. Then. LIH = aL, and LCH = uLc, which

implies that IH = al and CH = oC. So, from (3.25), XH = ooe: from (3.28).


(WH //2) a o3; and from (3.22), s = o: so that sL, = LI and sLc = LCH. Refer to

Figure 3.3 for a graphical representation. The top parallel line represents the allocation

of labor to final goods production, Lp* = E/X, innovative activity, L,'. and

0 L Le L


0 R E

LH, -

Figure 3.3
Symmetric Case

imitative activity. Lc', in the integrated equilibrium. The bottom parallel line represents

the set of endowment points. OH is Home's origin; OF is Foreign's origin. For any

endowment point. E, OHE is Home's endowment of labor, and EOF is Foreign's

endowment. A diagonal line is drawn from OH to L and from E to L. Dropping

perpendicular lines from K and J to diagonal OHL forms similar triangles GJL. DKL and

OHOL. which makes GL/OHL = JL/OL, DG/OHL= KJ/OL, and OHD/OHL = OK/OL.

Similar triangles OHLE, OHGR, and OHDQ are formed by dropping lines parallel to LE

from D and G to OHOp. LPH, LIH and LCH are the allocations of labor to final goods


production, innovative activity and imitative activity respectively. By the properties of

similar triangles. LPH/Lp* = LIH/L`* = LCH/Lc' = OHE/OL = o. A similar diagram can

be constructed for the foreign country.

In addition to lending itself to convenient graphical representation, this symmetric

case also simplifies the trade balance. With EH 0 and w = 1,

EH LH + CpY a- L p Y (3.32)

is expenditure at home. Also, VH = oav, + avc = aV. and the service account must

balance (see equation 3.29). The shares of Home and Foreign expenditures. assets, labor

in imitative and innovative activities and in manufacturing are equal to their shares in

labor. So a and (1 s) (1 r) Equation 3.30 becomes
s- (I -s) o'(l ao) (1 O)a-- (3.33)

The merchandise trade account must balance if Home's proportion of manufacturing is

equal to its proportion of assets. which is equal to its proportion of labor.

In this symmetric integrated equilibrium, Home will export from cH,, H (and 3

industries if E, < EF or o < V). It will import from aF and 3F industries. Thus, this

model generates product cycles among different sized countries. For example, suppose

that an industry is dominated by a Home monopolist so that Home initially exports from

this industry. Suppose that a Foreign firm successfully imitates this monopolist's quality.

The Home and Foreign firms split the world market. If a is greater than one half. Home

will now import in this industry. Another industry may not experience product cycles.

A Home monopolist may be imitated by a domestic firm so that Home continues to

dominate and export from this industry. In still another industry, say a duopoly based


wholly at Home, a Foreign firm may capture the entire market share through innovation.

Consequently, Home may go from exporting to importing in that industry and may also

recapture some of the market through imitation.

In general, Home and Foreign market shares fluctuate across industries. aHCFdt

Home monopolists lose half their market shares to Foreign imitators in dt, and acCHdt

Foreign monopolists lose half their market shares to Home imitators. Also.

2(fH //2)lFdt Home duopolists lose their total market shares to Foreign innovators.

and 2(3F -1 /2)IHdt Foreign duopolists lose their total market shares to Home

innovators. The pattern of trade fluctuates and has richer possibilities than a model of

endogenous innovation alone. In particular, it is possible, in this model, for a country

to capture part or all of the market in some industry and lose part or all of the market

in other industries during the same period.

In each interval, dt. Foreign imitators successfully transfer technology from

c.HCFdt = ((l-a)a'C'dt Home monopolists, and Home successfully transfers technology

from Foreign monopolists in acCHdt = (l-a)oa'C*dt industries. In the symmetric case.

these transfers are equal. Let 4H ( F ) be the proportion of duopoly industries in which

Home (or Foreign) has successfully transferred technology from a Foreign (or Home)

monopoly. Then,

at fCH 3I' ^ (la)af3- (1 u)a (3.34)

A similar calculation gives 3pF (1 a) /3' and H /3 OF The transfer of

technology from Home to Foreign (and vice versa), and the associated transfer of market

share, are related to the global intensities of imitative and innovative activity. For given


levels of I* and C*, the endowments of labor endogenously determine the extent of

technology transfer. a = /2 maximizes these transfers. Intuitively, the more equally

endowed the two countries, the more they interact.

Proposition 7

The pattern of trade, under the assumption of symmetry, fluctuates stochastically,

involves two- \way endogenous international technology transfer and product cycles (when

a # V), as well as intranational endogenous technology transfer. The extent of both

technology transfer and product cycles is determined by the intensities of global

innovative and imitative activities and relative national labor endowments.

3.5 Conclusion

This paper constructs a Neo-Schumpeterian model of growth and trade between

advanced countries. The model emphasizes the roles of costly and risky innovation and

imitation, and incorporates instantaneous diminishing returns to each R&D activity.

There is industrial targeting for R&D in which industries undergo cycles of innovation

followed by imitation. Spillovers from innovation to imitation occur because unit costs

of imitation are lower than those for innovation. Spillovers from imitation to innovation

occur because R&D experience gained from imitative R&D activity lowers the costs of

subsequent innovation. In this model, the integrated equilibrium can be achieved by free

trade, with no DFI and no trade in R&D services.


The results of this model can be compared to previous work. In contrast to

Grossman and Helpman (1991a), trade occurs under FPE. and innovation and imitation

can occur in both countries. This allows the possibility of richer patterns of trade.

These patterns of trade are similar to those in Dinopoulos et al. (1993), but there is no

costless transfer of technology, a characterization consistent with the Industrial

Organization literature on diffusion. In particular, the present model allows for

technology transfer in both directions and for countries to capture part of the market in

some industries, instead of the entire market.


4.1 Introduction

[A]cademic and policy discussions...might be more fruitful
if we spent less time working out solutions to systems of
equations and more time defining precisely what the words
we use mean.
Romer (1993)

Neo-Schumpeterian growth literature may not hinge on the existence of sizeable

R&D knowledge spillovers, but they make the theorist's life easier. Consequently,

empirical investigation into the nature, magnitude, and extent of spillovers of knowledge

from R&D activity currently attracts a lot of attention. Detection of R&D spillovers is

also important for accurate measurement of the social returns to R&D--critical for

optimal R&D policy discussions. Nowhere, however, is the possible presence of

spillovers more interesting than in the interactions among countries. It matters for

foreign investment policy, national industrial policy, and international intellectual

property rights protection. The new growth theory further suggests that strategies that

increase the flow of spillovers will accelerate growth. Thus, it presents the enticing


possibilities of rapid economic development for some less developed countries and

increased efficiency for fully integrated economies.

Unfortunately, these spillovers are extraordinarily difficult to identify and

measure, despite numerous efforts to do so. Part of the problem is that theoreticians

generally use exogenous spillover effects as a tool in their models rather than focus on

theoretical examination of the forces that influence or are influenced by these spillovers.

Additionally, because of the host of observability and definitional problems surrounding

the concept of international R&D knowledge spillovers, empirical work is problematic.

The theoretical and empirical importance of these spillovers was touched on in section

1.4 of Chapter 1. The current chapter is meant to address the question: what are

spillovers and how do we measure them? The focus is on international, intraindustry

R&D knowledge spillovers.

The main thrust of this chapter is to dispel the prevalent notion that spillovers are

an unlocked for and costless boon to recipients; that, once acquired by one agent, the

marginal cost of knowledge to other agents is close to zero. Just sitting in the physics

section of the library does not make one a physicist. The prospective scientist must

invest time and money.' Just so, firms must invest in R&D activities to copy the

innovations of other firms in the industry. They may spend less because of information

acquired as a result of the previous success, but if they do not engage in R&D activity,

they will not enjoy any pure spillover benefits. Alternatively, firms may maintain small

'Notwithstanding the possibility that playing tapes while you sleep or sleeping on a
book may have some positive but costless effect.


investments in various auxiliary R&D programs that are designed to position the firm

so as to maximize any expected spillover benefits from possible innovations by rivals or

related industries. Studies that do not recognize these expenditures may present biased

estimates of the magnitude of spillovers.

This chapter builds on the model of the previous chapter in order to clarify the

issues involved in defining and measuring R&D knowledge spillovers. It is relatively

straightforward to define a national quality index or stock of knowledge for the model

presented in Chapter 3. An equation of knowledge accumulation can be derived and

compared with estimated equations, in the existing literature, which attempt to measure

international spillovers. I conclude from this comparison that the existing studies are

not capturing true spillover effects because they do not distinguish between innovative

and imitative R&D activity or account for other diffusion expenditures. Furthermore,

'spillover-seeking' behavior by profit maximizing firms militates against the presence

of sizeable free-rider benefits from spillovers.

Section 4.2 discusses the meaning of R&D knowledge spillovers in detail.

Section 4.3 extends the model of Chapter 3 to an operational equation of national

knowledge accumulation which is compared to existing studies. Section 4.4 discusses

issues of spillover measurement. Section 4.5 concludes.

4.2 What Are Spillovers?

Knowledge is nonrivalrous and at least partially nonexcludable, so it is no surprise

that externalities, or spillovers, are associated with its production. What muddies the

waters are the presence of more than one type of the flow commonly referred to as R&D

spillovers, and, of course, the unobservable nature of knowledge. These various flows

have different consequences for theory and policy so it is important to distinguish

between them. I use Figure 4.1 to identify these flows and the associated spillover


Innovative R&D activity results in some new or improved process or product.

Four benefit flows can be distinguished. The first stream includes all direct benefits that

the innovator captures through (temporary) market power associated with the innovation.

These flows may include profits from sales of superior products, productivity gains, and

licensing. This stream, resulting from market transactions, is perhaps the easiest to

measure. It represents the private return to R&D. When added to the three remaining

flows, the result is the social return to R&D.

The second stream is direct benefits to customers of new products or existing

products for which prices have dropped due to process innovations and competition.

Because monopoly power is imperfect, and because the innovator may not foresee all of

the uses of the new product, customers will not in general, pay the full value of the

innovation. This second flow is a pecuniary externality associated with the product. It


Innovative New Product
R&D or Process


Benefit to

Benefit to

Benefit to

Current Competitiors

Benefit to
Future Innovators

Figure 4.1
Benefit Flows From Innovation

arises because of market imperfections, competition, and measurement errors, not

market failure. Accurate measurement of this potentially large benefit stream is

essential for the calculation of the social return to R&D. Identifiable in principle, this

flow is harder to measure than the first benefit stream. It does not represent, however,

true R&D knowledge spillovers, although often measured as such.

Griliches distinguishes between the spurious spillovers of flow 2 in Figure 4.1 and

what he calls true spillovers: "ideas borrowed by research teams of industry i from the

research results of industry j." (1992, p. S36) Of course, i can equal j, and 'industry'

can be replaced by 'firm.' Because I distinguish between innovative R&D activity and



imitative R&D activity, I further categorize these 'true' spillovers into two types

according to the type of R&D activity of the recipient:2

The third flow is knowledge transfers to current competitors, who cannot be

prevented from duplicating the new product or process at lower R&D cost. To the extent

that competitors must devote resources to this noncooperative technology transfer, this

is a measurable flow which is an externality to the innovator, not to the recipient. But,

to the extent that the costs of imitating are lower than the costs of innovating because of

the nonexcludable nature of knowledge, these are free-rider spillovers from (primarily)

innovative activity to (primarily) imitative activity.3 These are static spillover effects in

the sense that they do more to affect current market structure than future knowledge

accumulation. If innovation and imitation costs vary independently with the level of

activity, the magnitude of these spillovers is endogenous.

The last benefit flow identified in Figure 4.1, flow 4, is the benefit to future

innovators. This is the spillovers concept most often employed in the new growth

models to overcome any long-run diminishing returns to R&D. It is also the most

difficult flow to identify and measure, since it is related to the intertemporal, public-good

2The stylized model of Chapters 2 and 3 envisions major innovations followed by
exact duplication by imitators. In reality, imitators may make minor improvements to
differentiate their products or improve a process while adapting and adopting it. These
relatively minor changes could be interpreted as innovations in another model and may
sum to substantial increments in knowledge. Individually, however, these 'imitations'
will not have the same impact on knowledge production as major innovations.

3These spillovers are not just from reverse engineering or weak patent laws. The
reduction in uncertainty, arising from the simple knowledge that a particular line of
research was fruitful to a competitor, may be important, allowing the imitator to conduct
a narrower research program.


nature of knowledge. These spillovers arise because those firms engaged in current R&D

activities add to the stock of knowledge. This is a key factor in affecting future

innovation in that industry and others. But, the ways in which these spillovers actually

occur are difficult to quantify. They are of a different, more elusive, quality than the

nonexcludability spillovers of flow 3 in Figure 4.1. It is not simply a matter of it being

easier to copy than to create. It is picking up clues as to the nature of the unknown,

which illuminate the most effective path to the next stage, competitive arena or state-of-

the-art in the industry.4 How can this effect be detected, especially if internalized by

firms currently at the state-of-the-art, either through innovation or imitation, and engaged

in a race to discover the next state-of-the-art in the industry?

There is both theoretical and empirical evidence that intraindustry transfers of

this type require recipient R&D expenditures to be able to take advantage of any new

additions to the knowledge stock.5 Simultaneously engaging in similar innovative

activity may position the firm to take advantage of spillovers from a rival, but

concurrent maintenance R&D activity or subsequent imitative activity, or both, are

substitutes for innovative activity in this role (flow 5 in Figure 4.1). Further, if the

innovation is major, unsuccessful rivals may still require expenditures to copy the

successor to maintain their R&D competitiveness and market share. Familiarity with the

4Kortum (1995) suggests a search model of innovation in which successful research
spills over to subsequent research by shifting the underlying distribution of undiscovered
techniques, thus maintaining the pool of potential improvements.

5 See Cohen and Leventhal (1989), Henderson and Cockburn (1995), Nadiri (1993),
and Griliches (1992) on this point.


current state-of-the-art seems essential. So, in principle, these spillovers are also

associated with R&D activity on the receiving end and are therefore endogenous.

4.3 Acquired Knowledge or Spillovers?

In this section I use the model previously developed in Chapters 2 and 3 to

interpret current efforts to measure spillovers. Recall that, in this model, endogenous

innovative and imitative R&D contribute to long-run growth in consumer utility through

quality improvements. Both are Poisson processes with endogenous arrival rates. I =

I(L), (C C(Lc) ) is the arrival rate or intensity of innovative (or imitative) activity per

industry, L, ( Lc) is labor employed in innovative (or imitative) activity per industry ,

and I'(L,)>0, C'(Lc)>O, I"(L,)<0, C"(Lc)<0. There is free entry into each activity,

firms are atomistic, and industries are targeted first for innovation and then for imitation.

Below I reproduce the key equations of the integrated equilibrium:
7rL Cvc
v, = u1 (4.1)

vc c = uc (4.2)
(P + I)
Equations 4.1 and 4.2 are the zero-profit conditions (ZPC) for innovative and

imitative activity, respectively, in the steady state, where rL are dominant firm profits,

rc are collusive profits, p is the discount rate, and u, (or uc) is the unit cost of

innovative (or imitative) activity. Equations 4.1 and 4.2, along with a labor constraint

(not reproduced here), completely describe the integrated equilibrium steady state.


In this model, with free trade between two advanced countries (Home and

Foreign) and international capital mobility, growth in consumer utility is always equal

in the two countries. A quality index can be defined, however, for which the global

growth rate is equal to growth in consumer utility. A distinction can be made between

this growth rate and the growth rates of national quality indices. Define the global

quality index or stock of knowledge as

Atf =Jln.'A dto (4.3)

where ht(w) is the state-of-the-art quality in industry w at time t, w e [0,1], and In X is

the knowledge increment associated with each state-of-the-art product. Then, Appendix

G shows that

A =T3**lnX g' (4.4)

where g', given in (3.19), is the steady-state rate of growth of global consumer utility,

I" is the steady-state level of innovative activity or the mean rate of occurrence of

innovations, and 0* is the steady-state percentage of industries targeted for innovation,

given in (3.11). The rate at which the world quality index grows equals the proportion

of industries targeted for innovations, times the mean rate of occurrence of innovations,

times the knowledge increment of each innovation. This growth rate is always equal to


Compare this with the growth rate of Home's stock of knowledge. Home's stock

of knowledge is

AHt = fnjh" )do (4.5)


where hHt(o) represents the highest quality available in Home from domestic firms in

industry w at time t. In the steady state,

AH = (apCH + IH)1n (4.6)

where cF, is the percentage of Foreign monopolies targeted for imitation by Home firms,

CH' is the level of Home imitative activity per industry, and IH* is the level of Home

innovative activity per industry in the steady state. Home increases its stock of

knowledge from both innovation and technology transfer from abroad through imitation.

The term

FaCH (4.7)

represents the rate of technology transfer from abroad through imitation.

The national growth rates of knowledge can be compared to the global rate under

the symmetric case already examined in Chapter 3. Recall that a is Home's share of the

world labor endowment, and s is its share of final goods production. In the symmetric

case, r= s, aF = (1-a)a', CH = oC', and I'H = al', so that

AH = (aC* + P'IH)lnA = (2-a)ag > ag" (4.8)

for a greater than zero. Home's stock of knowledge, and consumer utility, grow faster

than its share of innovation would imply due to the costly international transfer of

technology through imitation. So, even among advanced countries, international

technology transfer is an important element of growth.

Equation (4.6) can be compared with a class of papers attempting to measure

international spillovers of knowledge by estimating an equation of the general form

G = 6,RH + FRF + c, (4.9)


where G is growth in total factor productivity (TFP) or labor productivity, R, is some

measure of Home R&D activity such as expenditures, Rp is a measure of similar foreign

R&D activity and Ec is an error term. The parameter 5 is thought to measure spillovers

from foreign or borrowed R&D.6 This equation is meant to measure the relative

importance of Home and Foreign R&D for national productivity growth. Rewrite (4.6)


AH = XcC + XIIH + E, (4.10)

where A = In ., X, = InX, and e2 is an error term. The impact on knowledge from the

two sources is allowed to vary. An equation such as this can be estimated for the U.S.

across industries and over time (time and industry subscripts omitted).

AH is the gross increment in knowledge per period. This variable is not

directly measurable, but a reasonable proxy could be the change in industry stock market

value per period. If the degree of appropriability of the firm vis-a-vis the consumer is

relatively constant, this method might sufficiently capture the net increases in the value

or quality of the industry's products. Let AH = CS + E3 where S is the change in

stock market value in each period. If is constant across time and the variance of E3 is

6See Nadiri (1993) and Griliches (1992), for discussions of this literature.

7In principle, other technology expenditure flows, such as patent purchases and
licensing should also be considered. See Nadiri (1993) for evidence that these flows have
increased. See Kokko (1994) and Saggi (1994) for discussions of spillovers associated
with DFI.


small, this will be a reasonably good measure of the growth in quality or knowledge

attributable to innovation.8

There are advantages to this approach. First, directly estimating the effects of

R&D activity on firm value, not its impact on productivity, leaves aside the problem of

separating out the effects of learning-by-doing and human capital accumulation, which

do not have the observability of R&D, nor the news event characteristic of innovation.

Second, this approach is not limited to process innovations, for which only a nonconstant

portion of R&D is undertaken.9 Third, it reduces the possibility of inadvertently

capturing 'spurious' spillovers through incorrectly measured input prices (type 2 flows

in Figure 4.1); the problem of correctly deflating R&D expenditures to obtain measures

of real R&D activity is still present. Fourth, it reduces the timing problem of when

R&D affects productivity. R&D news will be immediately incorporated into stock

market values. Many studies use cumulative R&D flows to alleviate this difficulty,

8 An alternative is to use some quality adjusted patent count. See Griliches (1992)
for a discussion of the shortcomings of patent data. Patents are said to be a noisy
measure of innovative output. Some innovations aren't patented. Not all patents have
value, and their value varies over time. Current received wisdom is that regressions of
firm value on measures of R&D input perform better than such regressions with patent
counts as the dependent variable. See Thompson (1995b). There have been recent
attempts to improve our understanding of the relationship between innovation and
patents. See Eaton and Kortum (1994) for a model of technical change and diffusion
across countries in which the decision to patent is endogenized.

9Thompson (1995b) develops a model in which an innovation directly affects firm
value, thus capturing the effects of both process and product innovations. The reduced
form of his model also includes current profits as a determinant of firm value.
Alternatively, a model of process innovation equivalent to the model developed in
Chapters 2 and 3 could be used. In this case, A, is equivalent to TFP growth.


which is especially problematic because the effects of foreign R&D may have longer lags

than own R&D effects.

In equation 4.6, CH is per industry imitation activity, and aU is the percentage of

foreign monopolies targeted for imitation. Similarly, IH is the per industry innovative

activity, and 0 is the percentage of firms targeted for innovation. In practice, the

intensity of R&D activity and its impact on the stock of knowledge will vary across

industries, and innovative and imitative activity will occur simultaneously in each

industry.10 So, in (4.10), ap* = I' = 1 and Kc measures the average impact on the

national knowledge stock of primarily imitative activity directed at noncooperative

technology transfer from abroad in each industry. The impact of Home innovative

activity is 1 ."

Note that, in (4.9), RH = CHF + CHH + IH. The difference between X1 and 6H

is that 65 measures the impact of all Home R&D activity, forcing X1 = ic, and

overmeasuring, by CHH, the R&D activity directed at increasing the national knowledge

stock. By similar reasoning, 6, measures the effect of foreign R&D, RF = CF + I,,

without recognizing that CF should have little effect and without considering the costs of

bringing about these 'spillovers' (namely CHF). In contrast, RF does not enter into (4.10).

'"See Klenow (1994) for a model that explains cross industry variations in R&D
activity through variations in technological opportunity, market size, and appropriability
of innovations. See Davidson and Segerstrom (1994) for a model qualitatively similar
to that of Chapter 3 but in which innovation and imitation occur simultaneously in each

"A term could also be added that measures aggregate national imitative activity to
test the assumption, made in Chapter 3, that imitative activity may directly contribute to
the stock of knowledge, through learning-by-doing in R&D.


Much of what is considered spillovers may be costly transfers, which can be estimated

through diffusion expenditures. 5H may underestimate the effectiveness of IH, and bF

may not be accurately capturing spillover effects.

To illustrate this last point, ignore the differences between the left-hand side

(LHS) of equations (4.9) and (4.10), or assume AH = G, as in footnote 9. Suppose that

Home innovation can be related to total Home R&D, and the intensity of imitation of

Foreign innovations is positively related to the intensity of foreign innovation:

IH = aRH + e, a
and CF = bRF + e.

Substituting these into (4.10), and comparing the result to (4.9) shows that, if (4.10) is

the true model, then 5H = aXIH < X1H, SF = bc 1 Xc, and E, = E2 + ,el +4-ce2.

Note that the effectiveness of Home innovative R&D, 1H, is underestimated by 6H ,

and 6F is inaccurately capturing the effectiveness of Home imitative R&D, which may

include spillovers from Foreign R&D. Furthermore, Variance(e,) > Variance(E2).

These facts imply that equation (4.10) should improve over (4.9).

The question is, then, how to allocate expenditures between substantially

innovative activity and substantially imitative activity. If this cannot be done efficiently

and satisfactorily, then estimating equation (4.11) will not improve over (4.10). One

possibility is to allocate by size of research programs. It could be assumed that small

programs are, primarily, maintained in order to facilitate spillovers, while large programs


are innovative.12 This separates R&D activity into imitative and innovative activity, but

the proportion of imitative activity directed at foreign firms must be determined. If there

are adequate data on patent infringement complaints, then the ratio of foreign complaints

against domestic firms to total complaints against domestic firms, Z, can provide an

estimate of CH .13 Then,

^H C= CH + (4.11)

Finally, C, and I, must be converted from unobserved intensities of R&D activity

into R&D expenditures. Suppose that, instead of the specific functional forms of

Chapters 2 and 3, CH and IH take the following forms:

CH = acLCH (4.12)

and IH = aLi (4.13)

Since the primary purpose is not to measure diminishing returns to R&D, assume that

0 = 4, for which estimates are provided for 16 industry groups by Thompson (1995b).

Substituting for these in (4.12) and (4.13), and using (4.11), allows (4.10) to be rewritten


S = YILH + Y2LI + 5 ,(4.14)


'2This could be expensive and time-consuming, of course, requiring a high degree
of disaggregation, but this regression could be done for a single industry. Henderson and
Cockburn (1995), for example, have collected such data for the pharmaceutical industry.

"Alternatively, since imitators must often license some key component, licensing data
may be useful.


2 ,a

E2 E3 E4

LeH and Lm can be interpreted as innovative and imitative R&D expenditures,

respectively. These are allocated, as discussed above, by research program size, and

may be measured with error, but E(E5) is still zero. The variable is constructed from

patent infringement data, licensing data, or other data that might be used to distinguish

between imitative activities directed at Home and Foreign firms.

From examination of (4.14) and (4.15), distinguishing between these R&D flows

is important. Notice that even if Xc = X1, 0 = 0, and a, = ac, then y, yz, because

only a fraction of imitative activity is directed at foreign firms. y, and 72 measure the

impact on the quality or knowledge index of imitative activity that transfers technology

from abroad and innovative activity that creates knowledge at home. If Xc = X,, as

implied by the model, and 0 = 4, then yi / > 72 implies that ac > a,. In what sense,

then, can this be called a measure of the magnitude of spillovers from innovators to

imitators? This is the topic of the next section.

4.4 Measuring Spillovers

For the model used here, type 4 spillovers in Figure 4.1 are exogenous. Type 3

spillovers, however, those from innovators to imitators are endogenous, at least in the

sense to be explained below. If ac in (4.12) is greater than a, in (4.13), and 0 = 4), the

same level of effort gives a higher probability of successful imitation than innovation.

If the only factor of R&D production is labor, which is the num6raire, (4.12) and (4.13)

imply unit costs of
1 1/e 0 -
uc -= C = a cCo (4.16)
uI = aI' (4.17)


SI = -- (4.18)
SMF = u (4.19)

be defined as the magnitude of intraindustry spillovers from innovators to current

competitors at the industry and firm levels respectively. Equation 4.18 is exogenous,

presumably determined by such effects as industry specific appropriability characteristics

and information technology. In (4.19), unit costs are determined in equilibrium (as

indicated by *) at the industry level, by, among other things, L the world labor


endowment. S, could also be affected by intellectual property rights protection,

subsidies and firms' expectations about future profits.

If firms are atomistic, then they take (4.19) as given. If SM < 1, then there are

exogenous spillovers at the firm level as well. But,

SM, = (4.20)
U. V.
and vc* < v,*, by construction, in this model. Since the successful imitator splits the

market with the innovator, the expected discounted benefits to imitation cannot exceed

the expected discounted benefits to innovation. Of course, this need not be generally


In any case, S, # S. except by coincidence (or if unit costs are constant, which

is not borne out by the substantial empirical evidence of instantaneous diminishing returns

to R&D)14. So, if the regression described in section 4.3 is carried out and an estimate

of SM is obtained, it must be interpreted as occurring at the industry level. Firm level

type 3 R&D spillovers from innovative activity to imitative activity, SM, may be larger

or smaller than those which occur at the industry level." Which measure of spillovers

to use matters depends on the context. S. is independent of policy; Sm is not.

'4See Griliches (1992), Nadiri (1993), Thompson (1995b), and Henderson and
Cockburn (1995) for evidence of instantaneous diminishing returns to R&D.

"This discussion assumes, as in Chapter 2 and 3, that u,' and c' are determined
independently and at the industry level. How realistic this assumption is depends on
industry specific characteristics. It may take specific skills to run smaller programs
designed to duplicate another's success as cheaply as possible, as compared to running
large innovative projects. If these specific skills are in fixed supply and firms are small
and competitive, then these costs will be independent.


The magnitude of spillovers from innovators to imitators is important for the

discussion of North-South trade. There are many models that imply that imitation coupled

with production cost advantages is an effective course of economic development. 6 The

larger the magnitude of spillovers, the more effective this course of development. A key

issue is the possible existence of a geographic dimension to spillovers. In

(4.18), ac may be a function of distance from the innovating firm or country because,

say, spillovers work partially through the labor markets. This is a natural barrier to

foreign competition, which may be counteracted by the foreign government through

policies which affect S,. These may include designing intellectual property rights

protection laws that favor imitators or subsidizing imitation.

This type of spillover also matters for national patent law and optimal R&D

policy. In welfare considerations, the benefits of imitation are usually considered to be

lower prices and increased variety. These are balanced against the incentives to

innovate. A complicating factor is the existence of the innovation to innovation

spillovers of type 5 in Figure 4.1. To the extent that imitators can expect spillovers to

their own innovative activity and incorporate these expectations in vc, they will increase

their imitative activity. This imitation may be the most efficient means of staying

competitive in R&D, and this consideration must also be balanced against the incentives

to current innovators.

'6See, for example, Grossman and Helpman (1991a) and Barro and Sala-I-Martin
(1995), Ch 8.


Although this chapter does not model spillovers from innovation to innovation of

type 4 in Figure 4.1, it does offer some observations. A dominant theme of the chapter

has been the necessity of engaging R&D activity in order to benefit from spillovers. Just

as imitators may incorporate anticipated spillovers into expected benefits, vc, innovators

will incorporate them into v,. Cohen and Levinthal build a model in which "absorptive

capacity represents an important part of a firm's ability to create new knowledge," and

in which "spillovers may encourage [innovative] R&D under some conditions." (1989,

pp. 570, 574)

This 'spillover-seeking' behavior by innovators complicates the discussion of

optimal R&D policy further. Increasing the ease of dissemination of knowledge may

increase innovation. Moreover, these increased expenditures may lower the magnitude

or value of anticipated spillovers. For type 3 spillovers, in Figure 4.1, if vc is large

relative to v1, firm level spillovers will be small, even if industry level spillovers are

large. If the magnitude of type 4 spillovers per innovation does not increase with the

level of innovative activity ( v, does not increase with I) the same effect can occur


Evidence that firms engage in efforts to capture spillovers abounds. Nadiri (1993)

reports that a significant proportion of R&D conducted in the U.S. is done by foreign

firms--possibly attempting to counteract any geographic spillover disadvantages. Nadiri

also reports an increase in recent years of joint ventures in R&D. One motive for these

ventures is to internalize potential spillovers. Henderson and Cockburn (1995) provide


evidence that economies of scope in the pharmaceutical industry may be generated by

intrafirm spillovers.

The implication of this behavior is that there may not be as much of a role for

strategic industry policy based on spillovers as popularly conceived. Firms will

inevitably have superior information about the magnitude and direction of potential

spillovers than the government (or economists) and will incorporate this information into

their decisions. The market imperfections associated with knowledge production and

dissemination may not be as large as commonly believed, at least in well developed

markets. 7

4.5 Conclusion

This chapter is concerned with the meaning and measurement of international

intraindustry R&D knowledge spillovers. Because there seems to be some confusion in

the literature as to the precise nature of R&D knowledge spillovers, I spend some time

discussing the concept. I develop an equation of knowledge accumulation through

innovation and costly technology transfers from abroad. This is compared to existing

efforts to detect international spillovers of knowledge. I conclude that many existing

'7Thompson (1995a) looks at the consequences of industrial espionage and piracy for
international relations. He cites the example of Chinese firms illegally producing bootleg
compact disks and computer software, infringing on U.S. firms' copyrights. He points
out that the gravity of the situation is due to the implicit involvement of the Chinese
government in a 'policy of piracy.'


measures of spillovers are biased and that spillover-seeking behavior by firms engaged

in R&D lowers the magnitude of ex ante spillovers.

Future work includes testing the knowledge accumulation equation developed in

the paper to see if it improves over existing studies in measuring the relative importance

of technology transfers from abroad. It also remains to endogenize innovation to

innovation spillovers, both intra and interindustry, and attempt to ascertain their avenues

of transmission and magnitudes. Finally, it may be useful to develop a model in which

these spillover magnitudes are possibly affected by the avenue of international



Research sometimes poses more questions than it answers: mine is no exception.

Chapter 1 briefly addressed the question of whether there are long-run diminishing

returns to R&D. Of course, a lifetime of research may not answer this question, but it

is still worth asking. Sustained long-run growth is an important goal of many peoples.

This dissertation represents an increment of knowledge, however small, in understanding

this process and may even generate spillovers to future work. My efforts center on the

distinction between R&D activities focused on bringing about major breakthroughs

(innovative) and those directed at duplicating existing products or processes (imitative).

This distinction, when introduced by Segerstrom (1991) into the quality ladders

model of Grossman and Helpman (1991b), provided an interesting opportunity to e\plore

the art of modeling. In Chapter 2. I showed that sufficient instantaneous diminishing

returns to each R&D activity (innovative and imitative) are necessary for stability and

'normal' comparative statics in Segerstrom's model. There is considerable empirical

supportt for the existence of diminishing returns to R&D. but it is not clear whether

innovative and imitative costs are determined separately, as implied by the model. If

innovation and imitation require separate skills, their relative intensities could be affected

by differential subsidy.


More possibilities for new research are uncovered in Chapter 3. The international

transfer of technology and its influence on trade patterns among advanced countries are

the subject of that chapter. Considerable generalization of the model is possible. The

R&D technology used is rather limiting because it implies that unit costs are determined

at the global level. If different technologies are used, allowing R&D unit costs to be

determined at the national level, trade patterns can be analyzed when FPE doesn't hold.

Can a range of relative endowments be determined for which the collusive equilibrium

can be sustained, even with small wage differentials?

Another useful endeavor is to introduce alternative avenues (to imitation) of

international technology transfer and explore the effects of policy on the relative

importance of these different avenues. Costly DFI can be introduced, as can the

possibility of licensing. In a model of process innovation, for example, is the magnitude

of potential spillovers maximized through encouraging DFI, imitation. or some

combination? Does the answer depend upon the degree of similarity between the relevant

countries' tecIlhnoIly \ bases?

This last question leads to yet another implication of the model of Chapter 3. The

assumption of an exogenous learning-by-doing effect, by which imitative R&D plays a

vital role--not just in diffusing current technology, but in refining the research techniques

vital for future innovation--begs for formal modeling. There are dual aspects to this

learning. First, for the successful finn (or country). and, to a lesser extent, all engaged

in the imitation race, achieving the end product--knoit ledge--allows the firm (or country)

to travel closer to the technology frontier. This would seem to be a necessity if the firm